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In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl, 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest Ω-stable matrix problem: given an LMI region $ \Omega \subseteq {\mathbb C} $ Ω ⊆ C and a matrix $ A \in {\mathbb R}^{n \times n} $ A ∈ R n × n , find the nearest matrix to A whose eigenvalues belong to Ω. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices. [ABSTRACT FROM AUTHOR]

This paper investigates the examination of global asymptotic stability pertaining to uncertain complex-valued stochastic neural networks (UCVSNNs) with multiple time delays. This paper employs the real-imaginary separated activation function to establish an equivalence between complex-valued neural networks (CVNNs) and two real-valued activation functions, representing the real and imaginary parts respectively. This equivalence is utilised to analyse the original UCVSNNs model in a comprehensive manner. The global asymptotic stability of the studied UCVSNNs model is ensured by constructing an appropriate Lyapunov-Krasovskii generalised function and applying the $ It\hat {o} $ It o ˆ formula, linear matrix inequality (LMI) and other analytical techniques to derive the system stability and other sufficient conditions. In the meanwhile, we provide two numerical examples to demonstrate the reliability and benefit of the discovered results. [ABSTRACT FROM AUTHOR]

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results. [ABSTRACT FROM AUTHOR]

This work examines a polytope-type approach for observer-based security control of a fractional-order system that is under multiple attacks via an event-triggered scheme. A novel multiple-attack model is first proposed for fractional-order systems such as denial-of-service attacks and reply attacks, which can destroy the system's security during the signal process. In contrast to previous studies, the design of the controller is developed using an observer-based event-triggered scheme in the presence of multiple attacks. An event-triggering strategy is proposed to reduce the communication burden of the output measurement signals. An observer-based control is designed to keep the fractional-order system stable in all scenarios where one or more simultaneous attacks may occur. These findings can ensure the absence of Zeno behaviour and considerably reduce data transmissions. By employing the suitable Lyapunov–Krasovskii functional, sufficient conditions are derived to ensure fractional-order system stability. Controller and observer-gain matrices are obtained by using the linear matrix inequality technique. Finally, two examples are provided to demonstrate the feasibility and usefulness of the suggested methodology. [ABSTRACT FROM AUTHOR]

In this paper, the energy-to-peak filtering problem for the uncertain discrete-time singular bilinear systems is studied. This paper considers the uncertainties that consist of real systems and the possible data packet dropouts when performance output signals and measurement output signals are transmitted over digital channels. In the course of the study, the phenomenon is elucidated utilising the Bernoulli random binomial distribution. The goal is to design the desired filter, so that the filtering error system is admissible, and meets the specified energy-to-peak performance index. The design conditions of energy-to-peak filters for uncertain discrete-time singular bilinear systems are given by introducing the Lyapunov function and using linear matrix inequalities (LMIs). The impact of uncertainty on singular bilinear systems is addressed using a two-step approach. At last, a numerical illustration is provided to demonstrate the validity of the design. [ABSTRACT FROM AUTHOR]

In this study, we investigate how natural environmental conditions affect a training vessel using a 'mathematical model of wind and wave' specific to Lake Silm near Kamionka, Poland. Wind and wave measurements on the lake were conducted. We present the vessel's trajectory under varying conditions: navigating in restricted waters simulating port conditions with speed readings, and during propeller operation. The control system of the nonlinear autonomous object employed two controllers: a linear matrix inequality controller and an overriding trajectory controller. We assess the impact of nonlinearities in the measured waves. It is shown that the maximum entropy probability distribution conforms more closely to the empirical frequency histogram than the Gaussian distribution. The wave height probability distributions diverge from Rayleigh distributions, indicating slight nonlinear effects. These results enhance the mathematical model of Silm Lake's wave dynamics. [ABSTRACT FROM AUTHOR]

This study focuses on examining the issues of extended dissipative-based composite anti-disturbance reliable tracking control for stochastic Takagi–Sugeno fuzzy systems afflicted by sensor faults and multiple disturbances. Explicitly, the multiple disturbances include the autonomous Wiener process and non random noises with partly known information that are generated by an exogenous plant. To address the difficulty of estimating the non random disturbance while considering the partially known information, the study incorporates a fuzzy stochastic disturbance observer. Furthermore, to solve the output tracking issue of the system under consideration, a modified repetitive tracking control is implemented. Then, combining the methodologies of disturbance observer-based control technique with modified repetitive control, a composite anti-disturbance reliable tracking control strategy is developed for achieving the intended tracking goal despite the multiple disturbances and sensor faults encountered. Additionally, the proposed approach involves extended dissipativity scheme, which includes $ H_\infty $ H∞, passivity, dissipativity, and $ \mathfrak {L}_2 - \mathfrak {L}_\infty $ L2−L∞ performances in a unified framework. In particular, by employing Lyapunov–Krasovskii functional approach, the essential stability criteria for the proposed closed-loop system are articulated in the form of linear matrix inequalities. Additionally, numerical illustrations are presented to exemplify the application and efficiency of the developed control protocol. [ABSTRACT FROM AUTHOR]

This paper addresses the co-design of event-triggered dynamic output-feedback (DOF) control for discrete-time linear parameter-varying (LPV) systems. Two independent event-triggering schemes are introduced to determine when to transmit data from the sensor to the controller and from the controller to the actuator channels. Enhanced conditions employing linear matrix inequalities (LMIs) are derived to establish constructive criteria for simultaneously designing the gain-scheduled DOF controller and the triggering mechanisms, ensuring the asymptotic stability of the closed-loop LPV system's origin. Additionally, a convex optimisation problem is proposed to enlarge the inter-event sampling on the independent channels of sensor-to-controller and controller-to-actuator. Numerical examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The simultaneous fault detection and control (SFDC) has emerged as a reliable scheme. However, what happens when the designed structure undergoes changes? Such variations have the potential to cause instability and misdiagnosis. This paper delves into a cutting-edge SFDC structure that surpasses conventional designs in terms of reliability. The proposed Resilient Simultaneous Fault Detection and Control (RSFDC) structure considers variations in the designed parameters and provides a more robust and fault-tolerant approach to SFDC, with important implications for the design of reliable and resilient control systems in a broad range of applications. This scheme is formulated as a multi-objective optimisation problem, encompassing control and diagnosis objectives. Specifically, it aims to minimise the impact of faults and disturbances on the controlled output while reducing residual sensitivity to all changes and maximising the fault effects on the residual. Through simulation comparisons, this paper showcases the merits of the RSFDC structure in two examples, highlighting its superiority over other designs. [ABSTRACT FROM AUTHOR]

In this paper, based on event-triggered control, the stabilisation problem of time-varying delay switched linear system with all subsystems unstable is studied. Firstly, the idea of event-triggered mechanism is introduced, and the state feedback controller is designed. Combining the discretised linear Lyapunov function method with the average dwell time technique, the stabilisation schemes for continuous switched system with unstable modes are obtained. Secondly, compared with existing results, the event-triggered mechanism scheme adopted under the current event-triggered control strategy reduces the number of system triggers, effectively saves computational resources, avoids Zeno's behaviour, and has better performance in terms of sampling frequency. Finally, the idea of event-triggered mechanism is first extended to discrete time-varying delay switched systems where all subsystems are unstable. By solving linear matrix inequalities, sufficient conditions for global exponential stability of the system are obtained. The effectiveness of this method was verified through a simulation example of a turbofan engine model. [ABSTRACT FROM AUTHOR]

A new approach for the synthesis of polytopic $ L_{2}-L_{\infty } $ L 2 − L ∞ filters is proposed for uncertain systems over Finite Frequency (FF) ranges. The novelty derives from the use of FF specifications combined with the $ L_{2}-L_{\infty } $ L 2 − L ∞ performance index: First, conditions are provided for the asymptotic stability of the polytopic augmented systems, by trace calculation of matrices and the use of Finsler's Lemma. Then, synthesis conditions are proposed as LMIs for the polytopic filter parameters over several FF intervals. Furthermore, the use of slack matrices through Finsler's Lemma provides design conditions with less conservative outcomes. A numerical example is solved and simulated to demonstrate the effectiveness of the ongoing approach when compared with previous results in the literature. [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 research endeavour's primary attention is on the problems of stabilization and multiple disturbance rejection for a class of interval type-2 fuzzy stochastic systems that are prone to parameter uncertainties and multiple disturbances. Specifically, the multiple disturbances are classified into two aspects: the first aspect is matched disturbances, which emanate from an exogenous system, while the second aspect is norm-bounded mismatched disturbances. Further, to provide a precise estimation of the matched disturbances, a fuzzy rule-based multiple disturbance observer is built. Based on the estimated information from the framed observer, a disturbance estimation-based resilient control is devised that can withstand the effects of disturbances. Besides, the footprints of mismatched kind of disturbances are handled by employing the $ (\mathcal {Q},\mathcal {S},\mathcal {R})-\tilde \varsigma $ (Q , S , R) − ς ~ dissipative performance. Moreover, to insure the attainment of the foremost objective of this analysis, a collection of suitable criteria has been developed by means of linear matrix inequalities with the satisfied disturbance attenuation index through Lyapunov's theory of stability. In addition, under the lighting of adequate conditions, the gain matrices of the configured controller and the framed observer can be determined. Finally, two simulation examples are supplied as a conclusion to the examination, each serving to illustrate the potency and viability of the designed control scheme and the presented theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, the state observer for coupled cyclic genetic regulatory networks with time delays is designed. The coupling network is composed of two cyclic genetic subnets, which inhibit each other directly. By constructing a suitable Lyapunov – Krasovskii functional velated to the eyclic struction, the delay-dependent stability criteria of the error system are investigated in the form of linear matrix inequalities. Thereby, the state observer of the considered genetic regulatory networks is obtained. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the bivariate truncated moment problem (TMP) on curves of the form $ y=q(x) $ y = q (x) , $ q(x)\in \mathbb R[x] $ q (x) ∈ R [ x ] , $ \deg q\geq ~3 $ deg ⁡ q ≥ 3 and $ yx^\ell =1 $ y x ℓ = 1 , $ \ell \in \mathbb N\setminus \{1\} $ ℓ ∈ N ∖ { 1 }. For even degree sequences, the solution based on the size of moment matrix extensions was first given by Fialkow [Fialkow L. Solution of the truncated moment problem with variety $ y=x^3 $ y = x 3 . Trans Amer Math Soc. 2011;363:3133–3165.] using the truncated Riesz–Haviland theorem [Curto R, Fialkow L. An analogue of the Riesz–Haviland theorem for the truncated moment problem. J Funct Anal. 2008;255:2709–2731.] and a sum-of-squares representations for polynomials, strictly positive on such curves [Fialkow L. Solution of the truncated moment problem with variety $ y=x^3 $ y = x 3 . Trans Amer Math Soc. 2011;363:3133–3165.; Stochel J. Solving the truncated moment problem solves the moment problem. Glasgow J Math. 2001;43:335–341.]. Namely, the upper bound on this size is quadratic in the degrees of the sequence and the polynomial determining a curve. We use a reduction to the univariate setting technique, introduced in [Zalar A. The truncated Hamburger moment problem with gaps in the index set. Integral Equ Oper Theory. 2021;93:36.doi: .; Zalar A. The truncated moment problem on the union of parallel lines. Linear Algebra Appl. 2022;649:186–239. .; Zalar A. The strong truncated Hamburger moment problem with and without gaps. J Math Anal Appl. 2022;516:126563. doi: .], and improve Fialkow's bound to $ \deg q-1 $ deg ⁡ q − 1 (resp. $ \ell +1 $ ℓ + 1) for curves $ y=q(x) $ y = q (x) (resp. $ yx^\ell =1 $ y x ℓ = 1). This in turn gives analogous improvements of the degrees in the sum-of-squares representations referred to above. Moreover, we get the upper bounds on the number of atoms in the minimal representing measure, which are $ k\deg q $ kdeg ⁡ q (resp. $ k(\ell +1) $ k (ℓ + 1)) for curves $ y=q(x) $ y = q (x) (resp. $ yx^\ell =1 $ y x ℓ = 1) for even degree sequences, while for odd ones they are $ k\deg q-\big \lceil \frac {\deg q}{2} \big \rceil $ kdeg ⁡ q − ⌈ deg ⁡ q 2 ⌉ (resp. $ k(\ell +1)-\big \lfloor \frac {\ell }{2} \big \rfloor +1 $ k (ℓ + 1) − ⌊ ℓ 2 ⌋ + 1) for curves $ y=q(x) $ y = q (x) (resp. $ yx^\ell =1 $ y x ℓ = 1). In the even case, these are counterparts to the result by Riener and Schweighofer [Riener C, Schweighofer M. Optimization approaches to quadrature:a new characterization of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions. J Complex. 2018;45:22–54., Corollary 7.8], which gives the same bound for odd degree sequences on all plane curves. In the odd case, their bound is slightly improved on the curves we study. Further on, we give another solution to the TMP on the curves studied based on the feasibility of a linear matrix inequality, corresponding to the univariate sequence obtained, and finally we solve concretely odd degree cases to the TMP on curves $ y=x^\ell $ y = x ℓ , $ \ell =2,3 $ ℓ = 2 , 3 , and add a new solvability condition to the even degree case on the curve $ y=x^2 $ y = x 2 . [ABSTRACT FROM AUTHOR]

This paper deals with a new design problem of adaptive gain robust model-following/tracking controllers for a class of systems with matched and unmatched uncertainties via piecewise Lyapunov functions. In the proposed design approach, compensation inputs for matched and mismatched uncertainties for the system are introduced and the proposed adaptive gain model-following/tracking robust controller can achieve that the tracking error decreases asymptotically to zero in spite of uncertainties. In this paper, on the basis of the concept of piecewise Lyapunov functions, we show linear matrix inequality-based sufficient conditions for the existence of the proposed controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The looped-functional approach has been extensively used for stability analysis of sampled-data systems. For this approach, this paper introduces two new functionals to minimise the conservatism of stability conditions. The first one is called a non-negative integral functional (NIF) that is added to the derivative of a common Lyapunov functional. The second one is a general looped-functional (GLF), whose values at sampling instants are traditionally not well-defined, and are defined here in terms of their limits. Leveraging further affine canonical Bessel-Legendre inequalities expressed by simplified polynomials, a polynomial-based NIF, a polynomial-based GLF, and a polynomial-based zero equality are tailored for obtaining hierarchical types of stability conditions in the form of linear matrix inequalities. Finally, numerical examples show that: (i) the proposed functionals lead to less conservatism when compared with several state-of-the-art methods; and, (ii) the resulting stability conditions exhibit a hierarchical characteristic in the sense that the higher level of hierarchy, the less conservatism of the criteria. [ABSTRACT FROM AUTHOR]

This paper presents a new control method for surge instability of the compressor system. Due to the importance of the active control approach in improving the efficiency of the compressor system, a new scheme based on the model predictive control (MPC) technique has been considered to control surge which gives the benefits of control signal optimization by considering the constraints on states and input. Because of designing a novel MPC by using of linear matrix inequality scheme, the optimization problem is solved in less time and with less complexity. The proposed method is able to consider the limitation of the close coupled valve actuator and also covers the uncertainty on the model. In addition, the developed model describes the nonlinear behaviour of the compressor system and handles the effects of the pipe on surge instability. Using Lyapunov theory, the stability of the closed-loop system under the proposed robust active controller is shown. The simulation results show the high pressure and high efficiency operation of the system under study in different operating conditions. [ABSTRACT FROM AUTHOR]

Free spectrahedra are dimension free solution sets to linear matrix inequalities of the form \[ L_A(X)=I_d{\otimes}I_n+A_1{\otimes}X_1+A_2{\otimes}X_2+\dots+A_g{\otimes}X_g\succeq 0, \]LA(X)=Id⊗In+A1⊗X1+A2⊗X2+⋯+Ag⊗Xg⪰0, where the $ A_i $ Ai and $ X_i $ Xi are symmetric matrices and the $ X_i $ Xi have any size $ n\times n $ n×n. Free spectrahedra are ubiquitous in systems engineering, operator algebras, and the theory of matrix convex sets. Matrix and free extreme points of free spectrahedra are particularly important. We present theoretical, algorithmic, and experimental results illuminating basic properties of extreme points. For example, though many authors have studied matrix and free extreme points, it has until now been unknown if these two types of extreme points are actually different. This paper settles that issue.We also present and analyze several algorithms. Namely, we perfect an algorithm for computing an expansion of an element of a free spectrahedron in terms of free extreme points. We also give algorithms for testing if a point is matrix extreme and for computing matrix extreme points that are not free extreme. [ABSTRACT FROM AUTHOR]

Pole placement with specified damping and decay rate is one of the primary criteria for ensuring good transient response. This control design problem has known solutions for continuous-time systems in terms of the linear matrix inequality (LMI) region. However, a systematic solution for a discrete-time system is an open problem due to the non-convexity of the constant damping locus. This paper addresses the problem of placing the closed-loop poles of linear discrete-time uncertain polytopic systems in a constant damping region. The non-convex damping region is approximated to an elliptical segment that represents an LMI region. Criteria for designing state and output feedback (static as well as dynamic) controllers are then derived. The effectiveness of the proposed approach is demonstrated with examples including a boost converter to improve its transient behaviour in the presence of input voltage and load variations. [ABSTRACT FROM AUTHOR]

This article investigates the problem of finite-time stability and stabilisation (FTSS) in time-varying stochastic systems with multiplicative noise and time-delays. To simplify research process, the method of dimension expansion is employed to transform systems characterised by constant delays into delay-free models, which enables the extraction of the finite-time stability (FTS) of the original systems by leveraging the FTS analysis conducted on the new model. Two distinct approaches are employed to establish criteria for determining FTSS in systems. The first approach leverages the state transition matrix (STM) method to acquire both necessary and sufficient stability conditions for the simplified models. Furthermore, sufficient conditions for the FTS of the original systems can be obtained. For ease of verification, our second approach integrates the Lyapunov equation with linear matrix inequalities (LMIs), offering a framework to obtain control gains. Finally, the proposed results are instantiated through three simulation examples to demonstrate their efficacy. [ABSTRACT FROM AUTHOR]

In this paper, the $ H_{\infty } $ H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and $ (x, u, v) $ (x , u , v) -dependent noises is studied. Firstly, the $ H_{\infty } $ H ∞ consensus problem is transformed into a standard $ H_{\infty } $ H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified $ H_{\infty } $ H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It $ \hat {\rm {o}} $ o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations. [ABSTRACT FROM AUTHOR]

To guarantee the stability and performance of an overall heterogeneous multi-agent system, feedback control structures must be capable of addressing the presence of heterogeneous agent-based nonlinear uncertainties, unknown actuation performance, and coupling effects. Additionally, some tasks require agents to track the leader's state and reach different states in a distributed way. Therefore, this paper proposes a distributed adaptive controller that drives a set of agents to user-assigned positions in the presence of the mentioned heterogeneous system anomalies. To address actuator dynamics, a hedging-based reference model is used to decouple adaptive updating from the actuator dynamics. To deal with the coupled dynamics, an observer-based estimation algorithm is proposed. Finally, the low-frequency learning method is used to deal with the high-frequency control response and, therefore, to obtain a better transient performance. The overall closed-loop system's stability is investigated using the Lyapunov Stability Theory, and the Linear Matrix Inequalities (LMI) technique is employed to identify stability limits regarding the actuator bandwidths of each agent. Illustrative numerical examples are presented to demonstrate the designed controller's performance in a heterogeneous uncertain multi-agent system's dynamics with unknown actuation capabilities and coupled dynamics. [ABSTRACT FROM AUTHOR]

This paper deals with the reliable finite-frequency $ H_{\infty } $ H ∞ control problem for switched systems with actuator faults and mode-dependent average dwell time (MDADT). The objective of designing reliable controllers is to guarantee the stability and robustness of the closed-loop system in the case of actuator faults. The actuator fault is solved using the convex combination method. A finite-frequency $ H_{\infty } $ H ∞ performance index is first defined in the frequency domain, and then a finite-frequency performance condition is derived by the generalised Kalman-Yakubovi $ \breve{c} $ c ˘ -Popov (GKYP) lemma. Combined with the MDADT approach and linear matrix inequality technology, a sufficient condition for the existence of a set of reliable finite-frequency $ H_{\infty } $ H ∞ controllers is derived. As a comparison, a sufficient condition is also given for the existence of a set of standard finite-frequency $ H_{\infty } $ H ∞ controllers. Finally, the effectiveness and feasibility of the proposed method are verified using a tilt-rotor aircraft. In addition, simulations and comparisons show that the designed reliable controller can stabilise the system even if actuator faults occur. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven predictive iterative learning control (DDPILC) for nonlinear nonaffine systems. First, we develop an iterative predictive model (IPM) where an iterative dynamic linearisation technique is introduced for addressing the strong nonlinearities and nonaffine structure. Then, an auto-regressive model is employed to estimate the unavailable parameter of IPM along with the iteration direction. Next, the outputs in the future iterations are predicted pointwisely over the finite operation interval that are further incorporated into the optimal objective function to obtain the optimal control input sequence. In addition, a constrained-DDPILC is extended for systems with I/O constraints which are reformulated as a linear matrix inequality (LMI). The two proposed methods do not have model requirement except for I/O data. Simulation study verifies the results. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time boundedness problem of switched linear systems under periodically intermittent control. Sufficient conditions are established to guarantee finite-time boundedness or finite-time stability of switched linear systems under periodically intermittent control. The proof procedures are implemented successfully resorting to piecewise Lyapunov functions. Based on the linear matrix inequality technique, the conditions are casted into a convex optimisation problem and therefore, they can be efficiently handled. The method proposed in this paper is a much potentially useful one in practice because of its economical and efficient nature that is easy to employ. Finally, two examples are given to express the validity and efficiency of the proposed methods. [ABSTRACT FROM AUTHOR]

This work addresses the tracking problem for nonlinear systems with unmeasured variables. We offer a new design methodology that is composed of a two-degrees-of-freedom scheme. The reference model must track a time-varying signal, and the controller employed can be regarded as one-degree-of-freedom. Then, based on the error between the outputs of the reference model and the plant, another controller is designed to ensure that this mismatch converges to zero. The reference model and the system are described as Takagi–Sugeno (TS) fuzzy models with nonlinear consequents (N-TS), which allows for separating measured from unmeasured variables. An advantage of the proposed scheme is that the controller for the reference model can be carried out using several methodologies from the literature, whereas the controller that governs the output error can be static or dynamic, whose design is based on Linear Matrix Inequalities (LMIs). Two examples are used to illustrate the validity of the developed control methodology and to compare it to another recent approach in the literature. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of H∞ performance analysis of 2D discrete singular stochastic system described by Roesser model which is challenging since it involves 2D random variables and the disturbance simultaneously. Sufficient conditions are established for the regularity, causality and stability of the system. The proposed results are expressed in terms of strict linear matrix inequalities. Furthermore, a mean square asymptotic stability with an $ H_{\infty } $ H ∞ disturbance level is developed. Simulation example is provided in order to illustrate the relevance of our approach. [ABSTRACT FROM AUTHOR]

We investigate the robustness, disturbance attenuation and performance capabilities of a Proportional-Integral-Retarded (PIR) controller when controlling a class of uncertain second-order systems with input disturbances. The purpose of this paper is to provide insight into the trade-offs between these conflicting requirements. This is accomplished by introducing simple delay-dependent stability conditions, expressed in linear matrix inequality form, which are used to establish the trade-offs in PIR control. In light of the obtained stability conditions, we show that improving performance comes at the cost of reduced robustness and disturbance attenuation. To our knowledge, this problem has not been addressed before and these new results provide valuable insights and systematic guidelines for designing these controllers with trade-offs in mind, thereby completing our current understanding of the tuning mechanisms in PIR control. Inspired by the application field of fuel-cell systems, experiments are carried out on a proof-of-concept switching converter prototype to demonstrate the relevance of the obtained results. [ABSTRACT FROM AUTHOR]

This paper deals with the observer design for a class of Interconnected Takagi–Sugeno (TS) systems with Immeasurable Premise Variables (IPV). We first investigate the D-stability of Luenberger-like interconnected multiple observers. However, the resulting constraints can be somewhat conservative due to the use of a common Lyapunov matrix. Then, the so-called Finsler's lemma is used to relax the D-stability conditions through the introduction of additional slack variables providing more flexibility and extra degrees of freedom. The designed conditions are expressed as Linear Matrix Inequalities (LMIs). The proposed approaches are applied in simulation to a Proton Exchange Membrane Fuel Cell (PEMFC) system and a four-tank system. [ABSTRACT FROM AUTHOR]

This paper studies the $ {H_\infty } $ H ∞ filtering problem for a class of discrete-time semi-Markov switching repeated scalar nonlinear systems with an event-triggered scheme. Considering the limitation of bandwidth, the mode-dependent event-triggered mechanism is introduced to determine whether the currently sampled sensor data is transmitted to the filter, in which the parameters of the event generator depend on the system mode. By means of a constructed time-varying Lyapunov function, the two stages of the systems jump instant and mode residence are analysed, and a linear matrix inequality technique is used to ensure the mean-square stability and $ {H_\infty } $ H ∞ performance of the filter error system. Accordingly, the co-design method of the mode-dependent time-varying filter and the event-triggered mechanism is derived for semi-Markov switching systems. Finally, a numerical simulation is given to illustrate the effectiveness and feasibility of the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This note investigates the adaptive security control issue for uncertain delayed semi-Markov jump systems (DSMJSs) within the framework of sliding mode control (SMC), in which the DSMJSs are affected by generally unknown transition rates (GUTRs), actuator failures (AFs) and cyber attacks. By the virtue of the strong approximation ability of neural network (NN), an adaptive NN-based SMC synthesis is carried out, which could not only force the state trajectories onto the proposed sliding surface but also ensure the DSMJSs operate as demanded in spite of the interference errors, structural uncertainty, hidden AFs, cyber attacks and GUTRs. Then, in view of the reachability of the proposed linear-type sliding mode surface (SMS), linear matrix inequalities (LMIs) and stochastic stability theory, a novel stochastically stable criterion for the resultant DSMJSs is obtained. At last, the single-link robot arm model is offered as an instance with simulation to illustrate the viability of the devised strategy. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor. [ABSTRACT FROM AUTHOR]

In this study, control and fault detection are examined for Takagi–Sugeno (T–S) fuzzy continuous-time systems with conic-type nonlinearity. In a conic-type dynamic system, Takagi–Sugeno fuzzy models are applied. A conic-type non-linearity must lie in an n-dimensional hyper-sphere with an uncertain centre to satisfy the restrictive condition. A combined error system of estimation and control error is obtained by combining the observations and the controller. Our main goal is to design an observer and controller for fault detection that minimizes the impact of unknown inputs and faults on the system in terms of the $ H_{\infty } $ H ∞ performance. The Lyapunov function is used to construct the residual signal using an observer and a controller. Using Linear Matrix Inequalities (LMIs), we can express the performance conditions for $ H_{\infty } $ H ∞ . The scheme's effectiveness is demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

A new adaptive observer is proposed for a class of uncertain time-delay parabolic systems. The uncertainties are located in both the state equation and the output equation which are also subjected to a distributed delay. Our algorithm is based on backstepping-like transformation and a classical persistent excitation condition. To illustrate the performances of this observer, simulation results are provided. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilisation of switched time-delay systems (STDSs) with exponential uncertainty. Based on the Hurwitz convex combination and the energy attenuation principle, an improved state-dependent switching strategy is proposed, which switches to the next modes to obey the minimum energy. This approach fully considers the system dynamic of subsystems, which is more general. Considering the complex switching and delay dynamics, a mode-dependent Lyapunov–Krasovskii functional (LKF) that contains a triple integral term is constructed. The generalised free-matrix-based integral inequality (GFMBII) is used to estimate the integral terms in the derivative of the LKF, and an improved delay-dependent stability criterion is established in the form of linear matrix inequalities (LMIs). Further, to guarantee the stability of the STDSs with a large time-varying delay, a controller that considers the time delay and the exponential uncertainty is designed. Under this controller, a less conservative delay-dependent robust stabilisation criterion for STDSs with exponential uncertainty is established. The validity of the proposed methods is validated by two numerical examples and an application in river pollution control. [ABSTRACT FROM AUTHOR]

In the paper, the exponential synchronisation for delayed Clifford-valued coupled switched neural networks via static event-triggering rule is studied. Firstly, the drive-response systems for delayed Clifford-valued coupled neural network models are established. So as to avoid the non-commutativity issue of Clifford number multiplication, the original n-dimensional Clifford-valued models are decomposed into $ 2 ^mn $ 2 m n -dimensional real-valued models. On this basis, the error dynamics system is constructed, and then some new sufficient conditions are presented of the exponential synchronisation for the considered neural network models by using Lyapunov–Krasovskii (L-K) functional approach and the technique of linear matrix inequality. Finally, the effectiveness of the results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This study aims to address the non-fragile exponential synchronisation problem of stochastic neural networks (SNNs). To cut down unnecessary control costs, a novel aperiodic intermittent-based impulsive control (APIIC) is designed in this investigation. Besides, the randomly occurring gain fluctuation (ROGF) is considered in APIIC, which satisfies certain Bernoulli distributed white noise sequences. By exploiting the Lyapunov approach and the average dwell-time technique, some sufficient criteria are derived in terms of linear matrix inequalities, which ensure that APIIC can achieve exponential synchronisation of SNNs with and without ROGF. More intriguingly, a technical definition of aperiodic window-based average impulsive interval is developed to cut back the conservativeness of these results. At last, the effectiveness of our explored results is confirmed by several numerical examples. [ABSTRACT FROM AUTHOR]

This article features the composite disturbance estimation and non-fragile hybrid-triggered control problems for continuous-time repeated scalar nonlinear systems prone to external disturbances. Priorly, the proportional integral observer comprising of both proportional and integral loops is incorporated to obtain better state estimations. Further, the external disturbance weakening the system performance is carefully estimated by deploying an improved equivalent-input-disturbance technique. Then, the availed disturbance estimate is blended into the control algorithm to exterminate the influence of the disturbance acting upon the proffered system. Next, a hybrid-triggered control comprised of a transition among event and time triggered paradigms are considered to reduce the network transmittance and also to simultaneously enhances the system outcomes. On top of that, the perturbations in controller gain matrix are taken into concern in order to make the controller more resilient towards redundant changes. Following that, utilising the Lyapunov theory, we obtain the mean-square asymptotic stability requirements for the developed system with the use of linear matrix inequalities and configure the gain matrices. Successively, the credibility of the synthesised control system is portrayed by exhibiting two numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we consider a new class of generalized fractional linear multidimensional state–space systems described by the Roesser model. We discuss a novel technique for analysing robust stability, focusing specifically on the stability of the closed-loop system in terms of the $ \mathcal {H}_2 $ H 2 and $ \mathcal {H}_\infty $ H ∞ norms. Both discrete-time and continuous-time cases are addressed across various regions of the complex plane. An extension of the bounded real lemma is proposed, dealing with both continuous and discrete cases. This lemma is used to provide sufficient conditions, in the form of linear matrix inequalities, to ensure stability margin for the perturbed system. Motivating examples are presented to demonstrate the effectiveness of our main results. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time boundedness (FTB) of linear time-invariant systems that are affected by a disturbance generated by an exosystem. By using a time-invariant quadratic Lyapunov function, Finsler's lemma and a dual system approach, new sufficient linear matrix inequalities (LMIs) conditions are given for analysis and synthesis for FTB. These results are extended: first, to finite-time stability (FTS) of linear time-invariant systems, second, to their input–output FTS associated, or not, to FTB. All the conditions are given in terms of LMIs, which make them easily tractable. Finally, the computational efficiency and the conservatism reduction of our approach are illustrated through an illustrative example. [ABSTRACT FROM AUTHOR]

This paper investigates the $ \mathcal {H_{\infty }} $ H ∞ filtering problem for a class of discrete-time singular Markov jump nonlinear systems against hybrid attacks via a fuzzy-model-based method, in which the hybrid attacks contain deception attacks and denial of service attacks. Two random variables subject to the Bernoulli distribution are used to describe whether the hybrid attacks are encountered during the measurement output of the original system being transmitted to the filter. By using linear matrix inequality technology and Lyapunov stability theory, some sufficient conditions are given to guarantee the considered systems are stochastically admissible and meet $ \mathcal {H_{\infty }} $ H ∞ performance index γ. The design approach of the secure filter and a specific form to acquire the expected secure filter gains are obtained, respectively. Finally, to demonstrate the effectiveness of the proposed approach, both a numerical example and a practical example are provided. [ABSTRACT FROM AUTHOR]

In this paper, $ \mathcal {H}_{\infty } $ H ∞ observer-based consensus for a class of nonlinear multiagent systems (MASs) with actuator saturation and input delays are estimated. A new delay-dependent region partitioning approach has been introduced in multiagent systems. The state information of the leader can be obtained by designing a distributed observer for each follower. Based on the state information of the follower and the estimated state information of the neighbouring agents, a distributed controller has been developed. With the help of a novel Lyapunov–Krasovakii functional (LKF), using a region partitioning approach combined with Wirtinger inequalities, a sufficient condition is established in terms of Linear Matrix Inequality (LMI). Finally, simulation examples are presented to the applicability of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered control for uncertain delayed neural networks (DNNs) with actuator saturation against deception attack is discussed. We propose a novel framework into which an event-triggered mechanism (ETM), actuator saturation, system uncertainty, and deception attack are combined. In the framework, the discrete ETM is employed to determine whether the sampled signal should be transmitted to controller so as to save network bandwidth, a random occurrence deception attack model satisfying Bernoulli distribution is introduced to construct the system robust, and actuator saturation is considered due to the actual complex network environment. Based on the framework, we discussed the stochastic stability of a novel delayed neural network model in a closed-loop system. By resorting to the appropriate Lyapunov–Krasovskii functional (LKF), we derive some new sufficient conditions for the stochastically stable of the system and obtain the gain of the system controller using efficient linear matrix inequality (LMI) method. Finally, a numerical example, in the end, demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This research aims to design a robust adaptive tracking controller for Chua's switched nonlinear circuit systems. The proposed adaptive composite nonlinear approach is modified in order to provide a robust controller with improved performance in the presence of uncertainties and input saturation. It is demonstrated that by employing an integral sliding mode controller that is based on a linear matrix inequality (LMI), the resultant closed-loop system can attain an exponentially boundedly stable. This technique ensures robustness to the impacts of uncertainties and input saturation and reduces the chattering phenomenon. Eventually, a simulation example of Chua's circuit system is utilised to reveal the performance and advantages of the offered approach. [ABSTRACT FROM AUTHOR]

In this paper, the problem of practical finite-time coordinated path following control of a multi-agent system in an uncertain Euler flow field is studied. The coordinated path following control system is decoupled into a path following sub-system and a coordinated formation sub-system. The uncertain Euler flow field is estimated by constructing an extended state observer. By embedding the extended state observer into the design of the finite-time controllers for both sub-systems, practical finite-time stability of the coordinated path following control system is proved. Simulation results are provided for validating the feasibility and effectiveness of the control method. [ABSTRACT FROM AUTHOR]

Product and supply chain systems are a class of complex nonlinear systems due to the uncertain demand fluctuation and unexpected events, and Takagi–Sugeno (T-S) fuzzy systems are suitable for modelling such product and supply chain systems with different production rates. According to the uncertainty customer demands, different subsystems which describe the corresponding production-inventory processes are orchestrated by the T-S fuzzy rule. Change control is designed to handle the supply chain blocking and event breaking caused by uncertain factors. Then, sufficient conditions are given such that the exponential stability with a prescribed bullwhip effect attenuation level can be guaranteed, and the control synthesis problem is transformed into the solvability of linear matrix inequalities for the product and supply chain systems. An example is introduced to verify the validness and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

A novel parameter-dependent anti-windup compensator is developed to improve the performance of a constrained model reference adaptive controller. The combined control structure solves the input saturation and stability problem for inertia-varying quadcopters. The control synthesis follows the conventional two-step anti-windup design paradigm where a nominal controller is designed without consideration of input saturation while the anti-windup compensator is designed to minimise deviations from nominal performance caused by saturated inputs. To account for the varying inertia of the quadcopter during package retrieval/delivery routines, inertia parameters of the vehicle/package are estimated with an online recursive identification technique. These estimates are used by the model reference adaptive controller and to schedule the parameter-dependent anti-windup compensator. Anti-windup performance and stability conditions are formulated as a set of parameter-dependent linear matrix inequalities, which when solved, yield a gain-scheduled anti-windup compensator that ensures stability and minimises deviation from nominal performance when saturation occurs. The effectiveness of the combined control scheme is demonstrated by simulations of an input-constrained quadcopter lifting a payload of unknown mass. [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]