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This article investigates the robust consensus problem for nonlinear multiagent systems against time‐varying false data injection attacks on actuators and sensors. First, the root‐mean‐square (RMS) theory is used to extend the assumption of the slow‐varying or constant attack signals to the case of time‐varying attack signals. Second, a novel distributed multivariate observer (DMO) is designed to estimate the followers' system states and the time‐varying attack signals on actuators and sensors. With the help of the outputs of DMO, a distributed robust consensus control arithmetic is proposed, which can compensate for actuator attacks and isolate sensor attacks so that exponential consensus and robust consensus are achieved. In particular, the robust performance of estimation errors and consensus errors is ensured by establishing the RMS gain index via linear matrix inequality, in which the zero initial conditions of estimation errors and consensus errors are not required. Finally, two simulation examples, including a network of four aircraft longitudinal dynamic systems, are given to verify the effectiveness of the proposed arithmetic. [ABSTRACT FROM AUTHOR]

This article is dedicated to event‐triggered anti‐disturbance control of networked control systems via a guaranteed cost triggering scheme. A distribution interconnected observer structure is built to estimate these unknown matched disturbances. A novel event triggered condition is constructed in terms of real‐time cost and averaged functions composed of observer states and the last successfully transmitted one. A composite control scheme is provided by an event‐triggered observer‐based state feedback controller and compensators for the matched disturbances. A sufficient condition in term of linear matrix inequality is supplied to ensure the asymptotic stability of the resultant closed‐loop system. A simulation is carried out to demonstrate the effectiveness of the proposed triggering control strategy. [ABSTRACT FROM AUTHOR]

Robust regulation is predictively investigated in time-delay models including uncertainties, non-zero reference, and disturbance. Hence, to handle the complexities induced because of the time-delays, disturbances, and uncertainties, enhancing the transient performance would be a main control goal. To this purpose, the required transient and steady-state specifications are achieved through an integral control structure with adjustable gains. The constraints on the signals and aims of the control algorithm are also described by some linear matrix inequalities. Guaranteeing the stability, a minimisation procedure is found to specify the predictive controller. Several simulations are performed to establish the effectiveness of the introduced plan in comparison with the similar strategy. [ABSTRACT FROM AUTHOR]

This paper presents a new dilated linear matrix inequality (LMI) representation to design a state feedback controller and a dynamic feedforward disturbance compensator for linear parameter-varying (LPV) systems. The improved LMIs are convex and finite-dimensional without any iterative approach. The designs are based on a new proposed equivalent bounded real lemma (BRL) by means of matrix dilation for LPV systems and uncertain linear systems under time-varying parametric uncertainties (TVPUs). This dilated BRL provides lower conservative results than existing methods in terms of robust stability. Accordingly, a dynamic disturbance compensator is designed in addition to a state feedback controller. This paper mainly focuses on the design of compensators against disturbances in addition to the design of state feedback controllers. The dynamic matrices of the compensator change with the time-varying parameters of the LPV or uncertain system during operation, assuming that the disturbances and the parameters are measurable or observable. The compensator can be designed to attenuate the disturbances/noises or to improve reference tracking. Finally, numerical and simulation outcomes are presented to prove both the effectiveness and lower conservativeness of the proposed LMIs. [ABSTRACT FROM AUTHOR]

In this article, we address the topics of fault reconstruction and robust fault‐tolerant tracking control for periodic piecewise polynomial uncertain systems with time‐varying delays, faults and external disturbances. In detail, the periodic piecewise polynomial learning observer system is configured with the intent to concurrently reconstruct the faults and immeasurable states of the system that is being considered. Precisely, the key intent of this study centers around in devising a robust fault‐tolerant tracking control to achieve the tracking performance of the system as intended with mixed H∞$$ {H}_{\infty } $$ and passivity performance. To this end, a robust fault‐tolerant tracking control is designed by incorporating the reconstructed faults and error feedback, which aids in vouching for the outcomes that were desired. Besides, by building the periodic piecewise polynomial Lyapunov–Krasovskii functional and making use of the matrix polynomial lemma and Wirtinger's inequality, certain adequate conditions are procured in the frame of linear matrix inequalities. Subsequently, the required gain values for the devised controller and the configured observer are found by using the established linear matrix inequalities. Ultimately, in order to attest the controller's intrinsic potential and relevance, numerical example along with the simulation results is supplied. [ABSTRACT FROM AUTHOR]

According to Logvinovich cavity dependent expansion principle, a cavity developed by cavitator has memory effect, which arises cavity deformation at aft part of a supercavitating vehicle and leads time delay of travel state. This delay affects the dynamic behavior through changing hydrodynamic and moment on the control surface, and even induces instability. This paper focuses on the time delay effect of the underwater supercavitating vehicle, and a simplified dynamic model of underwater supercavitating vehicle with delay was established. First, a planing force was simplified in straight level state, then a simplified model of supercavitating vehicle with delay in longitude plane was obtained. Taking depth, pitch angle, vertical speed and pitch rate as state variant, H ∞ state feedback controller was designed by linear matrix inequality (LMI) and Lyapunov stable theory was exploited to prove the asymptotic stability of the system. Simulation results show that, the controlled system is effectiveness for both simplified model and non-simplified model and it can track reference command signal. [ABSTRACT FROM AUTHOR]

This study introduces the design of a state-feedback controller for Linear Parameter Varying (LPV) systems in scenarios where exogenous parameters are not directly accessible, and the state vector is to be estimated. Instead of considering a static feedback gain, it proposes a method for estimating these parameters and synthesizing a parameter-dependent state-feedback gain that is robust against uncertainties in parameter estimation. The state vector used by the state-feedback controller, and some quantities required by the estimation law, are both obtained by a robust filter synthesized by LMI (Linear Matrix Inequalities). This paper outlines the estimation, filtering, and control laws, detailing the conditions necessary for ensuring convergence and stability. A numerical experiment and a 2 DoF torsional system application show the enhanced dynamic performance of the method when applied to uncertain dynamic systems. The findings highlight the effectiveness of the proposed approach in maintaining system stability and improving performance despite the inherent uncertainties in parameter estimation, offering a significant contribution to the field of robust control for LPV systems. [ABSTRACT FROM AUTHOR]

Summary: In this study, the problem of preview tracking control (PTC) was considered with regard to the linear parameter periodic systems (LPPSs) subject to previewed signals. First, the difference operator approach was extended to derive an augmented error system (AES). As a result, the PTC problem was transformed into a stabilization problem via state/output feedback. Second, sufficient conditions guaranteeing the closed‐loop stability of the augmented error systems were derived, and the design of a periodic controller with preview actions was proposed through the approach of linear matrix inequalities (LMIs). Finally, a numerical simulation was performed to illustrate the effectiveness of the proposed periodic controller. [ABSTRACT FROM AUTHOR]

This paper proposes a robust lateral control scheme for the path tracking of autonomous vehicles. Considering the discrepancies between the model parameters and the actual values of the vehicle and the fluctuation of parameters during driving, the norm-bounded uncertainty is utilized to deal with the uncertainty of model parameters. Because some state variables in the model are difficult to measure, an H ∞ observer is designed to estimate state variables and provide accurate state information to improve the robustness of path tracking. An H ∞ state feedback controller is proposed to suppress system nonlinearity and uncertainty and produce the desired steering wheel angle to solve the path tracking problem. A feedforward control is designed to deal with road curvature and further reduce tracking errors. In summary, a path tracking method with H ∞ performance is established based on the linear matrix inequality (LMI) technique, and the gains in observer and controller can be obtained directly. The hardware-in-the-loop (HIL) test is built to validate the real-time processing performance of the proposed method to ensure excellent practical application potential, and the effectiveness of the proposed control method is validated through the utilization of urban road and highway scenes. The experimental results indicate that the suggested control approach can track the desired trajectory more precisely compared with the model predictive control (MPC) method and make tracking errors within a small range in both urban and highway scenarios. [ABSTRACT FROM AUTHOR]

This study focuses on the problem of perturbation suppression and tracking control of nonlinear fractional order systems with time‐varying delay. To simplify the control process for such systems, the Takagi–Sugeno fuzzy model is used to describe the nonlinear fractional order delayed systems. Additionally, a modified repetitive controller is applied to develop an output feedback technique for the proposed systems. To ensure system stability, the study establishes new delay‐dependent stabilization conditions using a novel Lyapunov–Krasovskii functional (LKF). These stability conditions are expressed in formation of linear matrix inequalities (LMIs) by adopting a frequency‐distributed model transformation and some slack matrices. The proposed method demonstrates that the system output can track the desired input with ignorable error, while effectively rejecting disturbances. Finally, the efficacy of the proposed method is evaluated through simulations of the modified Chua circuit and the hydraulic turbine governing system (HTGS). [ABSTRACT FROM AUTHOR]

This paper deals with the problem of robust decentralized control of discrete-time nonlinear interconnected descriptor systems (IDS) under the influence of external disturbances. First, we utilize the Takagi–Sugeno fuzzy model (TSFM) to represent discrete-time nonlinear IDS. For controller design, a proportional-derivative (PD) feedback strategy is employed to formulate a decentralized fuzzy controller for the discrete-time Takagi–Sugeno IDS (DTTSIDS). Furthermore, robust and passivity constraints are incorporated into the controller design process to mitigate the effects of disturbances. Based on the Lyapunov function and free weight function methods, we can analyze the stability of the DTTSIDS. The proposed conditions are converted into Linear Matrix Inequality (LMI) conditions through Schur Complement technology so that we can solve the problem through MATLAB LMI-Toolbox. Finally, the effectiveness of the proposed methodology is demonstrated through three examples presented in the paper and a comparison with other existing studies is given in Example 3. [ABSTRACT FROM AUTHOR]

Master–slave teleoperation systems with haptic feedback enable human operators to interact with objects or perform tasks in remote environments. This paper presents a sliding-mode control scheme tailored for bilateral teleoperation systems operating in the presence of unknown uncertainties and time-varying delays. To address unknown but bounded uncertainties, adaptive laws are derived alongside controller design. Additionally, a linear matrix inequality is solved to determine the allowable bound of delays. Stability of the closed-loop system is ensured through Lyapunov–Krasovskii functional analysis. Two-degree-of-freedom mechanisms are self-built as haptic devices. Free-motion and force-perception scenarios are examined, with experimental results validating and comparing performances. The proposed adaptive-sliding-control method increases the position performance from 58.48% to 82.55% and the force performance from 83.48% to 99.77%. The proposed control scheme demonstrates enhanced position tracking and force perception in bilateral teleoperation systems. [ABSTRACT FROM AUTHOR]

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design. [ABSTRACT FROM AUTHOR]

The problem of robust nonfragile H∞ filtering for fuzzy fractional order (FFO) systems 0 < α < 1 with uncertainties is studied. First, a new sufficient condition of H∞ control for fractional order systems is given to overcome the shortcoming of solving the complex matrix. Then, based on the condition and the linear matrix inequality (LMI) approach, the conditions of robust H∞ control for FFO systems are proposed, which can guarantee the prescribed noise attenuation level in the H∞ sense. Furthermore, the FFO filter is constructed, and sufficient conditions are proposed for FFO filter systems. Finally, two examples are given to verify the effectiveness of our conditions. [ABSTRACT FROM AUTHOR]

This paper highlights the design of a controller established on estimated states for one-sided Lipschitz (OSL) nonlinear systems subject to output and input delays. The controller has been devised by involving Luenberger-like estimated states. The stability of the time-delayed nonlinear system is reckoned by assuming a Lyapunov functional for delayed dynamics and for which a delay-range dependent criterion is posed with a delay ranging between known upper and lower bounds. The time derivative of the functional is further exploited with linear matrix inequality (LMI) procedures, and employing Wirtinger's inequality for the integral terms instead of the traditional and more conservative Jensen's condition. Moreover, a sufficient and necessary solution is derived for the proposed design by involving the tedious decoupling technique to attain controller and observer gain simultaneously. The proposed methodology validates the observer error stability between observers and states asymptotically. The solution of matrix inequalities was obtained by employing cone-complementary linearization techniques to solve the tiresome constraints through simulation tools by convex optimization. Additionally, a novel scheme of an observer-based controller for the linear counterpart is also derived for one-sided Lipschitz nonlinear systems with multiple delays. Finally, the effectualness of the presented observer-based controller under input and output delays for one-sided Lipschitz nonlinear systems is validated by considering a numerical simulation of mobile systems in Cartesian coordinates. [ABSTRACT FROM AUTHOR]

This study presents novel formulations for ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust state‐feedback control synthesis for discrete‐time linear time‐invariant systems based on linear matrix inequalities. The proposed formulations require searching for two adjustment matrices. The synthesis formulations include other formulations from the literature as particular cases according to specific values of the adjustment matrices. We propose the application of evolutionary optimization to determine the optimal values of these two adjustment matrices. One approach to obtaining a single‐step formulation for static output‐feedback control synthesis is to transform a state‐feedback control synthesis formulation via the simple change of variables. The alteration of variables considered in this study requires an adjustment matrix. The adjustment matrix influences the performance of the resulting controller or the existence of a feasible solution to the problem. Here, we also propose the application of evolutionary optimization to determine the optimal value of this adjustment matrix and the two adjustment matrices of the proposed formulations to obtain the optimal ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust control system. Case studies verify that despite the increased complexity, the proposed formulations and the method required to tune them may be indispensable in achieving a robustly stable control system or an enhanced ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance for more intricate problems. [ABSTRACT FROM AUTHOR]

The presence of uncertainty in the converter model and controller parameters affects the system's stability and dynamic performance. This paper presents a comparative analysis of robust non‐fragile control based on (i) the Kharitonov method and (ii) the linear matrix inequality (LMI) technique so that the controller can cope with the effect of both uncertainties. The first approach based on Kharitonov theorem determines the robust performance region with guaranteed gain margin and phase margin under parametric uncertainty. The second approach (LMI technique) is based on devising a control law that can quadratically stabilize the closed‐loop system subject to uncertainties and satisfy the H∞ norm bound constraint on disturbance attenuation. Based on these two approaches, a robust non‐fragile PI controller is designed for voltage mode control of dc‐dc buck converter. The effectiveness of the control approaches is evaluated based on (i) robustness against large plant parameter perturbations and load disturbance and (ii) fragility against controller parameter perturbations. The performance of the designed controllers (using the Kharitonov method and the LMI technique) has been thoroughly evaluated and validated through simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper deals with the robust control problem for networked uncertain semi‐Markov jump systems over digital communication channel, where some complicated factors are considered in this framework, such as false data injection attacks, incomplete sojourn‐time information, and actuator fault. In network environment, these problems frequently occurred: (1) Data must be quantified before it is transmitted via digital communication channels, and (2) there is always the risk of cyber‐attack. Traditional controllers are not effective to solve the robust control design issue of uncertain semi‐Markov jump systems since the signal quantization and cyber‐attack will degrade control performance evidently. Then, a resilient controller is designed to guarantee the stable running of system with incomplete sojourn‐time information and the system resiliency to unsecure shared data. With the help of Lyapunov stability theory, sufficient conditions are derived in the form of linear matrix inequality, which can determine the gains of the resilient controller. Finally, the simulation examples about single‐machine infinite‐bus power system are given to explain the effectiveness and feasibility of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper studies the trajectory tracking of a constrained mobile robot under slippery conditions. The goal is to propose a controller for real‐time operations of time‐varying dynamics with insignificant execution time. Therefore, a Laguerre‐based model predictive control (LMPC) is designed, and robustness is provided with an linear matrix inequality (LMI)‐feedback controller. Moreover, a recursive least square (RLS) algorithm with a forgetting factor is utilized to identify the required parameters of the LMI‐based controller. LMPC and LMI‐based controller stability is achieved with suboptimal theory and Lyapunov function, respectively. This algorithm separates the nominal system and introduces new dynamics containing uncertainties. Furthermore, LMPC is removed from the online calculation, which dramatically reduces computation burden and time; consequently, online computation is dedicated to determining the LMI feedback. Simulations are provided to compare the proposed robust controller to its not robust counterpart. Finally, it is demonstrated that this controller diminishes the execution time considerably, making it incomparable to previous robust MPC strategies. [ABSTRACT FROM AUTHOR]

This paper proposes a multi-objective H2/H ∞ maximum power tracking control of a variable speed wind turbine to minimize the H2 tracking error and ensure the H ∞ model reference-tracking performance, simultaneously. The optimal condition is obtained via a boost converter use, which adapts the load impedance to the wind turbine generator. Thus, based on the fuzzy T-S model, a multi-objective Maximum Power Point Tracking (MPPT) controller is developed, ensuring maximum power transfer, despite wind speed variation and system uncertainty. To specify the optimal trajectory to follow, a TS reference model is proposed taking as input the optimal rectified DC current. The conditions of stability and stabilization are expressed in terms of linear matrix inequality (LMI) for uncertain and disturbed T-S models leading to determining the controller gains. Finally, an example of MPP tracking applied to a Wind Energy Conversion System (WECS) illustrates the effectiveness of the proposed fuzzy control law. [ABSTRACT FROM AUTHOR]

This paper investigates the non-fragile robust H ∞ control problem of nonlinear uncertain neutral stochastic Takagi–Sugeno (T–S) fuzzy systems with mixed time-delays. The uncertainties are norm-bounded and time-varying. Sufficient conditions for H ∞ performance analysis results of the delay-dependent condition is established via the Lyapunov–Krasovskii functional (LKF) technique and linear matrix inequality (LMI) method. Based on the H ∞ performance result, a desired fuzzy control is designed by solving LMIs. Finally, an example is provided to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel integrated path following control scheme for a 4-Wheel Independent Drive (4WID) autonomous vehicle that can adaptively change its mechanism according to the driving conditions. The proposed integrated system handles the lateral steering controller, longitudinal speed, and yaw moment controls considering tire force capacity of each corner. For the lateral controller, the cornering stiffness uncertainties and the transient performance are considered and combined into an H∞ robust controller based on linear matrix inequality (LMI) theory. A super-twisting sliding mode controller (STSMC) based longitudinal controller is designed to deal with disturbances and suppress chattering. When encountering extreme conditions, the active yaw moment controller with hierarchical structure is adaptively activated to prevent large deviation from the reference path and maintain the stability of vehicle. For the tire force allocation, an optimization algorithm is proposed, which has flexible equality constraints to coordinate the longitudinal and lateral motions according to the driving conditions. Simulations based on Carsim-Simulink co-simulation platform show that the proposed method is effective and has excellent performance in both normal and extreme driving conditions. [ABSTRACT FROM AUTHOR]

Uncertain grid impedance is often common in power distribution networks; therefore, it is crucial to design an efficient controller in this situation. An issue that frequently occurs is the problem of unpredictable grid impedance, which can cause voltage fluctuations, power quality problems, and potential damage to equipment. This work provides a systematic control strategy to tackle these issues by supplying well-regulated power from a DC source to an AC power grid. A linear matrix inequality (LMI)- based robust optimal control is proposed in this paper to provide stability to the inverter system without offset error at the output side. The convergence time to steady state is minimized by solving the LMI problem to maximize the eigen value of the closed-loop system with the inclusion of the uncertainty of the filter parameter and grid impedance. Furthermore, the uncertainties in this study include the potential variation of values for the filters and the grid's impedance. These uncertainties occur because the grid impedance can fluctuate fast in the event of a fault or termination of a transmission line, while the filter's impedance can also be affected by changes in operating temperature. The simulation study of this proposed control includes a comparison between wide and narrow uncertainty ranges, as well as a performance comparison under uncertain parameters. Furthermore, this approach exhibits a lower power ripple in comparison to existing PI control method. [ABSTRACT FROM AUTHOR]

Achieving the robust fixed‐time stabilization (FxTS) of uncertain reaction‐diffusion systems (RDSs) utilizing intermittent boundary control is a valuable and unresolved problem. This paper simultaneously considers the influence of the uncertainty of non‐diffusion and diffusion coefficients on RDSs and provides an effective solution for the treatment of the uncertainty of diffusion coefficient in the investigation of FxTS. Then, a fixed‐time control scheme is presented to stabilize uncertain RDSs within a fixed time, which incorporates the merits of intermittent and boundary control and reduces control costs in both the spatial and temporal domains. Besides, some sufficient conditions in the form of linear matrix inequalities are deduced to guarantee the robust FxTS of uncertain RDSs with Neumann and mixed boundary conditions, respectively, which contain and generalize some existing results. Finally, the validity of the intermittent boundary control scheme and the FxTS criteria developed in this paper are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper proposes an observer-based proportional Derivative (O-BPD) fuzzy controller for uncertain discrete-time nonlinear descriptor systems (NDSs). Representing NDSs with the Takagi–Sugeno fuzzy model (T-SFM), the proportional derivative (PD) feedback method can be utilized in the fuzzy controller design via the Parallel Distributed Compensation (PDC) concept, such that the noncausal problem and impulse behavior are avoided. A fuzzy observer is proposed to obtain unmeasured states to fulfill the PD fuzzy controller. Moreover, uncertainties and transient response performances are taken into account for the NDSs. Then, a stability analysis process and corresponding stability conditions are derived from the Lyapunov theory with the robust control method and the pole constraint. Different from existing research, the Singular Value Decomposition (SVD) and the projection lemma are utilized to transfer the stability conditions into the Linear Matrix Inequation (LMI) form. Because of this reason, the conservatism of the analysis process can be reduced by eliminating the restriction on the positive definite matrix in the Lyapunov function. By giving the proper center and radius parameters of the pole constraint in the O-BPD fuzzy controller design process, the expected transient responses can be obtained for different designers and different practical applications. Finally, the effectiveness and applicability of the proposed O-BPD fuzzy controller are demonstrated by two examples of the simulation. [ABSTRACT FROM AUTHOR]

To enhance the stability of the frequency at the sending terminal of the HVDC island during operation, a novel DC supplemental frequency robust controller is proposed in this paper. The proposed controller utilizes the fast controllability of a DC power supply to maintain system frequency stability. The identification of a low-order linearized model of the system can be obtained from a high-precision Prony algorithm based on the second derivative method (SDM). Subsequently, utilizing a robust design methodology based on linear matrix inequalities, an additional frequency robust controller is devised, striking a balance between optimal performance and robustness. This supplementary frequency robust controller exhibits a straightforward control structure with a modest order, making it readily implementable. Simulation experiments conducted within the PSCAD/EMTDC framework substantiate that the designed supplemental frequency robust controller significantly enhances the frequency stability of the sending terminal system. Furthermore, when compared with traditional proportional integral (PI) controllers, it demonstrates superior control efficacy and robustness against various types of faults under different operational modes. Even in interconnected operational modes, it continues to operate effectively. The research findings offer valuable insights for practical applications in islanded power systems. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of finite-time observer-based H ∞ control design of networked switched systems (NSS) subject to external disturbances via an event-triggered observation strategy. This triggering strategy is used to decide when the output measurements are sent to the observer over the communication network. By incorporating digital networks, the closed-loop system is modeled as a switched delayed system due to network-induced delays. By using the average dwell time (ADT) switching method with the Lyapunov–Krasovskii functional, several sufficient linear matrix inequalities (LMIs) conditions for the observer-based control synthesis are developed to guarantee the finite-time boundedness and the disturbance attenuation control performance of the resulting switched delayed system. Finally, an example is given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The stability and dynamic performance of the system are impacted by the uncertainties present in the converter model and controller parameters. This paper introduces a robust non-fragile control approach that addresses the influence of these uncertainties. The approach involves developing a control law that achieves quadratic stabilization of the closed-loop system while also satisfying the H∞ norm constraint for disturbance attenuation. Based on this concept, a robust non-fragile PI controller is designed explicitly for voltage mode control of a dc–dc buck converter. The effectiveness of the proposed control technique is evaluated from two perspectives: (i) its ability to withstand significant perturbations in plant parameters and load disturbances and (ii) its resilience in the presence of variations in controller parameters. The effectiveness of the proposed control scheme is validated using simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the boundary fixed-time stabilisation for delay reaction–diffusion systems (DRDSs). A new boundary controller is designed to achieve fixed time stability of DRDSs. Firstly, a boundary fixed-time controller is presented for DRDSs. Then based on the designed boundary controller, using Lyapunov functional method, fixed-time stability lemma and Poincaré's inequality, we obtain the criteria to guarantee the fixed-time stability of DRDSs. In addition, boundary fixed-time controller is proposed for uncertain DRDSs to reach robust fixed-time stability. Both the cases, the systems with or without uncertainties, are severally followed by a fixed time, which is an upper-bound of the settling time and irrelevant to the initial conditions. Finally, two simulation examples are given to illustrate the fixed-time stability of the controlled systems, which show the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this study, the issue of simultaneous fault detection and control (SFDC) for a class of switched linear systems with input and state delays is being addressed. A detector/controller unit (dynamic observer/observer-based controller) is suggested for a residual generation that simultaneously takes into account the control and fault detection objectives using specific performance indices. It is assumed that the delay will fluctuate within a range with a lower bound that is not zero. Based on a Lyapunov–Krasovskii functional (LKF), and thanks to the free-weighting matrix and projection lemma, a new sufficient condition for developing a new method is put forth in terms of a set of linear matrix inequalities (LMIs). To illustrate how well the suggested results work, the proposed method is applied to a vehicle roll dynamic. [ABSTRACT FROM AUTHOR]

This paper considers a linear continuous- or discrete-time dynamic object in the absence of its mathematical model. As is demonstrated below, a control law that suboptimally damps initial and (or) exogenous disturbances of such objects can be implemented based on experimental and a priori data. The approach involves the methods of robust control design and duality theory as well as the technique of linear matrix inequalities. [ABSTRACT FROM AUTHOR]

In this article, robust tracking and disturbance rejection problem for Takagi–Sugeno fuzzy systems with time delay and external disturbances are discussed. Specifically, proportional‐integral controller with an enhanced equivalent‐input‐disturbance technique is constructed to force the output trajectories to track the bounded reference input signal even in the presence of external disturbances. Further, the resulting fuzzy control system can be represented as an augmented system with state delay and uncertainties and the output tracking problem is transformed into stabilization problem of the augmented system. In the stabilization analysis, the considered fuzzy system does not share the same membership functions with the proposed control. Moreover, the delay‐dependent stabilization criteria for the addressed fuzzy system are presented in the form of linear matrix inequalities by the virtue of augmented Lyapunov–Krasovskii functional. To be specific, the symmetric matrices involved in the Lyapunov–Krasovskii functional need not be positive definite. Ultimately, three numerical examples are offered to support the validity of the established theoretical results. [ABSTRACT FROM AUTHOR]

A robust global fuzzy sliding mode controller is designed in this paper for the synchronization of non-linear systems with control input non-linearities (CIN) and uncertainties. A consistent global fuzzy sliding mode control (GFSMC) law is developed, which guarantees the suppression of the reaching phase and the presence of the sliding phase from the initial time. Chattering phenomenon, which is characteristic of customary sliding mode control (SMC), avoided by the on-line fuzzy regulation of the sliding surface in the controller, when the system is subject to disturbances and CIN. Finite-time boundedness (FTB) properties are designed with adequate conditions, which are entrenched in terms of linear matrix inequalities (LMIs) with the help of cost and Lyapunov functions. Numerical simulations for the synchronization problem of the chaotic modified Colpitt's system and Duffing system clearly show the good performance of the proposed control scheme. The present work provides a regular procedure to design GFSMC for a class of non-linear systems with CIN. [ABSTRACT FROM AUTHOR]

The Takagi–Sugeno (T–S) fuzzy model is a versatile approach widely used in system control, often in combination with other strategies. This paper addresses key control challenges linked to the T–S system and presents important considerations to ensure its successful application using the Lyapunov theorem. One crucial aspect is determining the optimal number of premise variables and selecting accurate fuzzy rules for the T–S model. Additionally, the theorem based on Linear Matrix Inequality (LMI) is developed to enable effective disturbance rejection. To enhance stability control, constraints are imposed on the output angle and control input of a rotary inverted pendulum (RIP). By integrating T–S fuzzy control, disturbance rejection, and input/output constraints, robust stability in controlling the RIP is achieved. Extensive simulations are performed to showcase the efficiency of the suggested method, and the simulation results are thoroughly discussed and analyzed to verify the efficacy of the control method. [ABSTRACT FROM AUTHOR]

In this paper, the desired yaw orientation for an autonomous underwater vehicle is attained by acquiring a cascaded control structure based on a robust optimal control algorithm with a backstepping approach. A robust state feedback optimal control law is designed to control the yaw rate. Hence, the desired yaw rate is intended to be obtained by the backstepping controller by controlling the desired yaw orientation. The implementation of the proposed robust control algorithm is formulated by using semi-definite programming. A linear quadratic regulator in terms of linear matrix inequality is designed to address the control problem. The design of robust optimal control law in the steering plane is achieved by considering an uncertain polytopic AUV system. Realization of the proposed control algorithm is conducted in MATLAB/Simulink environment using the YALMIP tool. Robust behavior is ensured by the proposed control algorithm while tracking the desired yaw. The robustness analysis is extended by considering the various ranges of specific uncertain parameters to highlight the efficacies of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

In this article, to enhance the transient performances in constrained uncertain systems, a control technique based on linear matrix inequality (LMI) is characterized to the robust integral composite nonlinear feedback (CNF) controller design. To achieve this aim, considering the inputs limitations and the uncertainties, the regulation is transformed into a minimization subjected to several LMIs. Solving an optimization in real‐time, the gains of the controller are calculated. So, the regulation and the disturbance rejection are effectively handled employing the presented control law. Compared with the existing integral methodology, the provided simulations validate the applicability of the robust integral CNF control law in uncertain systems. [ABSTRACT FROM AUTHOR]

In this study, a state feedback robust control strategy with time delay dependence for the uncertainty, fault, and input time delay of a vehicle's controllable suspension system is designed. Firstly, based on the working principle of the adjustable damping suspension system, the total damping force of the suspension is divided into "foundation damping force" and "controllable damping force", taking the adjustable damping interval as the constraint boundary, which varies with the actuating velocity. Furthermore, based on the sensitivity analysis of the input time delay's relationship with damping force disturbance, it exerts influence on the controllable damping force part. The associated uncertainty and fault are defined through linear fraction transformation and proportional gain, respectively, and the two are decoupled from the control mechanism. Then, based on the Lyapunov stability theory, a robust control law for the time-delay-dependent H∞ state feedback is designed and transformed into a linear matrix inequality convex optimization problem to solve. Finally, the feasibility and effectiveness of the proposed method are verified by designing different combinations of uncertainty and fault tests and by comparing and analyzing these with the time-delay-independent H2/H∞ robust control strategy under random and pulse road excitation. [ABSTRACT FROM AUTHOR]

Low-frequency oscillations (LFOs) pose a significant obstacle in achieving optimal power flow and utilizing transmission corridors in large interconnected power systems. In this study, linear matrix inequality (LMI) base robust H ∞ wide-area damping controller (WADC) is introduced to effectively address critical LFOs. The proposed WADC utilizes wide-area signals, which modulate the phase angle of a thyristor-controlled phase shifter device. To ensure that the concerned modes of LFOs lie in left half of the complex plane, a D-space sub-region approach is applied. However, using wide-area signals introduces time delays, which negatively impact the efficacy of the WADC; hence, a time delay compensator (TDC) is incorporated into the feedback path of the signals. The proposed approach involves four key steps: selecting feedback signals using a combined modal transformation and geometric approach, designing an appropriate TDC, building a generalized plant with mixed sensitivity weights, and solving the LMI. The dynamic efficacy is verified on IEEE 4-machine 11-bus system, and 10-machine 39-bus system. Poorly damped single and multiple critical modes are placed in the D-space region of interest with specified damping ratios viz. 10% and 15%. Furthermore, damping ratios of critical modes are maintained with TDC based proposed WADC while deteriorating with other counterparts. [ABSTRACT FROM AUTHOR]

The aim of this work is the design of a current control by means of state feedback, based on linear matrix inequalities (LMI), and it is applied in a DC-DC coupled inductors Buck-Boost modular converter, which has been widely used in distributed generation systems with renewable energy sources. This method considers constraints on the location of poles defined in the complex plane called d-stability. The closed-loop control system is implemented in Matlab® Simulink and validated under different test scenarios, where better dynamic performance is obtained, its operating range is extended, with shorter settling times and a better time-response, in contrast with the classical PI control technique. [ABSTRACT FROM AUTHOR]

An isolated electrical network with an independent local distributed generator is very sensitive towards the contingencies between load demand and supply. Although the network system has less complexity in term of structure, its stability condition is crucial due to its stand-alone operating condition. Hence, to monitor the stability of the network, total power deficit is the only variable that can be estimated. This study proposed to utilize the 𝐻∞ filtering problem to design an estimator that can estimate the total power deficiency. For verification, the design estimator was tested under two cases which are nominal case and parameter uncertainty case. In nominal case, the system parameters are assumed to be known while in parameter uncertainty case the system has contaminated with uncertain parameter where its admissible value is laying in a given polytope. With complying the linear matrix inequality (LMI) constraint, the main objective function of the 𝐻∞ norm was guaranteed with minimum upper bound. The results show that the dynamical behaviors of designed estimator successfully trace the actual power deficit signal at steady state with minimal estimation error. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new definition of sustainability that includes dynamics and equity. We propose a theoretical framework that allows finding a fair and sustainable strategy for all stakeholders. More precisely, the framework allows calculating a strategy which ensures that in the long run the interests of all the stakeholders are reconciled. In order to calculate a such a strategy, we model stakeholders and actors as dynamical systems in state-space form. Furthermore, we use robust control and linear matrix inequalities to calculate the desired strategy. We use several simulation scenarios to show the effectiveness of our proposed framework. [ABSTRACT FROM AUTHOR]

Abstract Modern network and communication technologies are essential for the implementation and operation of load frequency control (LFC) systems. The measurements of crucial LFC system parameters will be compromised by attackers, rendering data received by the defence inaccurate and causing frequency fluctuations or even system collapse. To detect the potential attack on measured data and keep the LFC performance, an adaptive event‐triggered scheme with fractional order global sliding mode control scheme is proposed in this paper. Furthermore, Markov theory is employed for the modelling process with energy storage to present a multi‐area LFC power system considering renewable energy and hybrid cyber attacks. Stability and stabilisation criteria are built by employing improved Lyapunov stability theory and second‐order Bessel‐Legendre inequality. Finally, a two‐area LFC system under hybrid cyber attacks and a modified IEEE 39‐bus New England test power system with 3 wind farms are simulated to explore the efficacy of the proposed method.

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

This article investigates robust non-fragile event-triggered sampled-data fuzzy (ETSDF) control for uncertain nonlinear delayed distributed parameter systems. Initially, a T-S fuzzy delayed partial differential equation model is presented to exactly describe the uncertain nonlinear delayed distributed parameter systems (DPS). secondly, a robust non-fragile ETSDF control strategy is proposed to reduce the unnecessary SD and cope with the uncertainties in controller and system. Then, based on an appropriate Lyapunov functional, the exponential stability conditions of closed-loop nonlinear delayed DPS via linear matrix inequalities are presented. Lastly, one example is presented to illustrate the design method. [ABSTRACT FROM AUTHOR]

A major challenge in multi‐agent formation is the issue of delay and uncertainty. This article investigates a robust formation control problem for linear multi‐agent systems with input delay and model uncertainty. The strategy adopted by an agent in the system aims to predict the delayed state using output information from neighboring agents over a fixed communication network and generate the control input from the predictor output. The predictor is employed using the finite spectrum assignment (FSA) technique. The overall strategy leads to a unified framework representation, and the multi‐agent formation control problem is simplified to a closed‐loop stability problem for an agent. The overall problem comes down to deciding two feedback gains: predictor gain and controller gain. For a perfect plant model, any choice of stabilizing gains can achieve formation. But when agent models are uncertain, the gains need to be derived from the solutions of linear matrix inequalities (LMIs) containing network information and delay. LMIs are obtained from the bounded real lemma and the gains obtained from the solution guarantee to maximize the H∞$$ {H}_{\infty } $$ norm bound of allowable perturbation, modeled as additive uncertainty, for a known delay size. Further, since the FSA technique is sensitive to discretization, a digital implementation of the overall scheme is elaborated, which may help to debug stability issues in the implementation process. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed ideas. [ABSTRACT FROM AUTHOR]

This paper proposes a robust H∞-LMI-based primary controller using the Linear Parameter Varying (LPV) modeling for an AC Islanded Microgrid (IMG). The proposed controller can regulate the frequency and voltage of the IMG under various scenarios, such as load changes, faults, and reconfigurations. Unlike most previous studies that neglected the nonlinearity and uncertainty of the system, this paper represents the system dynamics as a polytopic LPV model in the novel primary control structure. The proposed method computes a state-feedback control by solving the corresponding Linear Matrix Inequalities (LMIs) based on H∞ performance and stability criteria. The robust primary control is applied to a test IMG in the SIM-POWER environment of MATLAB and evaluated under different scenarios. The simulation results demonstrate the effectiveness and efficiency of the proposed method in maintaining the stability of the frequency and voltage of the IMG. [ABSTRACT FROM AUTHOR]

Mobility using wheelchair is a crucial feature for disabled people. Between a manual wheelchair and an electric wheelchair, there is a very interesting and promising solution consisting of an electrical kit that converts a manual wheelchair to an electric wheelchair. Autonomad‐Mobility is a company selling such kits, where the wheels are equipped with a brushless motor. It presents new possibilities for mobility, especially for crossing obstacles and running on different types of soil. Several methods have been tested, from linear to nonlinear ones including the linear parameter‐varying control framework. Nevertheless, the most dangerous and critical issue is to be able to produce a so‐called safe and robust swing‐up: the transition from standard mode (four wheels on the ground) to gyroscopic mode (the wheelchair balancing on the rear push‐wheels). The gyroscopic mode is a unique feature improving mobility by providing a way to overcome obstacles that would normally be unsurpassable due to the caster wheels. Whereas some results exist, the solution must be compatible with any wheelchair and any disabled person whatever is her/his height and weight. Robustness of this unstable feature is therefore the key point of the work knowing that "exact" modeling is unrealistic. With the model in descriptor form and using the quasi‐linear parameter‐varying framework new stabilization conditions formulated as linear matrix inequality constraints are developed for attaining the goal. Simulations and real‐time experiments demonstrate the interest of this approach. [ABSTRACT FROM AUTHOR]

In this paper, the resilient stochastic neutral state delay system with the Markov chain problem is examined. It offers output feedback control based on discrete state space delay and uncertainty that appear under traditional delay-independent conditions and exist under neutral stochastic state delays. Lyapunov theory can be used to solve the formulation x c (t) = x (t) - C x (t - τ) for the intended H ∞ control of a stochastic model. Its stochastically mean square stability is shown using linear matrix inequalities (LMIs). The efficiency of the suggested strategy is shown by simulation results. [ABSTRACT FROM AUTHOR]