Search

In this paper, we study a system of nonlinear tempered fractional differential equations with multi-point coupled boundary conditions. By applying the properties of Green's function and the operator and combining the method of matrix analysis, we obtain the corresponding Lyapunov inequalities under two Banach spaces. And, we have compared two Lyapunov inequalities under certain conditions. An example is given to verify our results. [ABSTRACT FROM AUTHOR]

This paper investigates the leader-following H ∞ consensus of fractional-order multi-agent systems (FOMASs) under input saturation via the output feedback. Based on the bounded real lemma for FOSs, the sufficient conditions of H ∞ consensus for FOMASs are provided in α ∈ 0 , 1 and 1 , 2 , respectively. Furthermore, the iterative linear matrix inequalities (ILMIs) approaches are applied for solving quadratic matrix inequalities (QMIs). The ILMI algorithms show a method to derive initial values and transform QMIs into LMIs. Mathematical tools are employed to transform the input saturation issue into optimal solutions of LMIs for estimating stable regions. The ILMI algorithms avoid the conditional constraints on matrix variables during the LMIs' construction and reduce conservatism. The approach does not disassemble the entire MASs by transformations to the Laplacian matrix, instead adopting a holistic analytical perspective to obtain gain matrices. Finally, numerical examples are conducted to validate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

Descriptor systems are more complex than normal systems, which are modeled by differential equations. This paper derives stability and stabilization criteria for uncertain fractional descriptor systems with neutral-type delay. Through the Lyapunov–Krasovskii functional approach, conditions subject to time-varying delay and parametric uncertainty are formulated as linear matrix inequalities. Based on the established criteria, static state- and output-feedback control laws are designed to ensure regularity and impulse-free properties, together with robust stability of the closed-loop system under permissible uncertainties. Numerical examples illustrate the effectiveness of the control methods and show that the results depend on the range of variation in the delays and on the fractional order, leading to stability analysis results that are less conservative than those reported in the literature. [ABSTRACT FROM AUTHOR]

This work proposes a design methodology for predictive control applied to the single-phase PWM inverter with an LC filter. In the design, we considered that the PWM inverter has parametric uncertainties in the filter inductance and output load resistance. The control system purpose is to track a sinusoidal signal at the inverter output. The designed control system with an embedded integrator uses the principle of receding horizon control, which underpinned predictive control. The methodology was described by linear matrix inequalities, which can be solved efficiently using convex programming techniques, and the optimal solution is obtained. MATLAB-Simulink and real-time FPGA-in-the-loop simulations illustrate the viability of the proposed control system. The LMI-based MPC reveals an effective performance for tracking of a sinusoidal reference signal and disturbance rejection of input voltage and load perturbations for the inverter subject to uncertainties. [ABSTRACT FROM AUTHOR]

This study takes a detailed look at various inequalities related to the Euclidean operator radius. It examines groups of n-tuple operators, studying how they add up and multiply together. It also uncovers a unique power inequality specific to the Euclidean operator radius. The research broadens its scope to analyze how n-tuple operators, when used as parts of 2 × 2 operator matrices, illustrate inequalities connected to the Euclidean operator radius. By using the Euclidean numerical radius and Euclidean operator norm for n-tuple operators, the study introduces a range of new inequalities. These inequalities not only set limits for the addition, multiplication, and Euclidean numerical radius of n-tuple operators but also help in establishing inequalities for the Euclidean operator radius. This process involves carefully examining the Euclidean numerical radius inequalities of 2 × 2 operator matrices with n-tuple operators. Additionally, a new inequality is derived, focusing specifically on the Euclidean operator norm of 2 × 2 operator matrices. Throughout, the research keeps circling back to the idea of finding and understanding symmetries in linear operators and matrices. The paper highlights the significance of symmetry in mathematics and its impact on various mathematical areas. [ABSTRACT FROM AUTHOR]

This paper presents an observer-based dynamic output-feedback controller design procedure using linear matrix inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state-feedback gains, and observer gains are coupled into a dynamic output-feedback optimal controller. The LMI set used in the two stages is matrix inversion free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case. [ABSTRACT FROM AUTHOR]

Sensors are a key component in industrial automation systems. A fault or malfunction in sensors may degrade control system performance. An engineering system model is usually disturbed by input uncertainties, which brings a challenge for monitoring, diagnosis, and control. In this study, a novel estimation technique, called adaptive unknown-input observer, is proposed to simultaneously reconstruct sensor faults as well as system states. Specifically, the unknown input observer is used to decouple partial disturbances, the un-decoupled disturbances are attenuated by the optimization using linear matrix inequalities, and the adaptive technique is explored to track sensor faults. As a result, a robust reconstruction of the sensor fault as well as system states is then achieved. Furthermore, the proposed robustly adaptive fault reconstruction technique is extended to Lipschitz nonlinear systems subjected to sensor faults and unknown input uncertainties. Finally, the effectiveness of the algorithms is demonstrated using an aircraft system model and robotic arm and comparison studies. [ABSTRACT FROM AUTHOR]

The scope of complex dynamical networks (CDNs) with dynamic edges is very wide, as it is composed of a class of realistic networks including web-winding systems, communication networks, neural networks, etc. However, a classic research topic in CDNs, the synchronization control problem, has not been effectively solved for CDNs with dynamic edges. This paper will investigate the emergence mechanism of synchronization from the perspective of large-scale systems. Firstly, a CDN with dynamic edges is conceptualized as an interconnected coupled system composed of an edge subsystem (ES) and a node subsystem (NS). Then, based on the proposed improved directed matrix ES model and expanded matrix inequality, this paper overcomes the limitations of coupling term design in node models and the strong correlation of tracking targets between nodes and edges. Due to the effect of the synthesized node controller and the auxiliary effect of the ES, state synchronization can be realized in the CDN. Finally, through simulation examples, the validity and advantages of our work compared to existing methods are demonstrated. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fault detection in DC microgrids in the presence of denial-of-service (DoS) attacks. To deal with the nonlinear term in DC microgrids, a Takagi-Sugeno (T-S) model is employed. In contrast to the conventional approach of utilizing current sampling data in the traditional event-triggered mechanism (ETM), a novel integrated ETM employs historical information from measured data. This innovative strategy mitigates the generation of additional triggering packets resulting from random perturbations, thus reducing redundant transmission data. Under the assumption of faults occurring within a finite-frequency domain, a resilient event-based H − / H ∞ fault detection filter (FDF) is designed to withstand DoS attacks. The exponential stability conditions are derived in the form of linear matrix inequalities to ensure the performance of fault detected systems. Finally, the simulation results are presented, demonstrating that the designed FDF effectively detects finite-frequency faults in time even under DoS attacks. Furthermore, the FDF exhibits superior fault detection sensitivity compared to the conventional H ∞ method, thus confirming the efficacy of the proposed approach. Additionally, it is observed that a trade-off exists between fault detection performance and the data releasing rate (DRR). [ABSTRACT FROM AUTHOR]

Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson's type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson's type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function. [ABSTRACT FROM AUTHOR]

The asymptotic synchronization of quaternion-valued delayed neural networks with impulses and inertia is studied in this article. Firstly, a convergence result on piecewise differentiable functions is developed, which is a generalization of the Barbalat lemma and provides a powerful tool for the convergence analysis of discontinuous systems. To achieve synchronization, a constant gain-based control scheme and an adaptive gain-based control strategy are directly proposed for response quaternion-valued models. In the convergence analysis, a direct analysis method is developed to discuss the synchronization without using the separation technique or reduced-order transformation. In particular, some Lyapunov functionals, composed of the state variables and their derivatives, are directly constructed and some synchronization criteria represented by matrix inequalities are obtained based on quaternion theory. Some numerical results are shown to further confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

This study aims to propose a sampled-data control technique, utilizing a linear matrix inequality (LMI) approach, to achieve string-stable vehicle platooning in a cooperative adaptive cruise control (CACC) system with communication delays. To do this, a decentralized sampled-data controller design technique that combines one controller using sensor measurements and another one utilizing vehicle-to-vehicle (V2V) communication, ensuring both individual and string stability, is proposed first. Next, a memory sampled-data control (MSC) approach is presented to account for transmission delays in V2V communication. Additionally, an improved Lyapunov–Krasovskii functional (LKF) is presented to improve computational complexity and sampling performance. The design conditions are formulated as linear matrix inequalities (LMIs) in the time domain, facilitating efficient stability analysis and optimization. Finally, vehicle platooning simulations are provided to validate the effectiveness and feasibility of the proposed technique. [ABSTRACT FROM AUTHOR]

In this paper, a linear matrix inequality (LMI)-based robust model predictive speed control (RMPSC) with a disturbance observer (DOB) is proposed to guarantee stability and control performance against the parameter uncertainty and disturbance of a permanent magnetic synchronous motor (PMSM). All external torques applied to the PMSM are defined as disturbance, estimated by the DOB, and used to construct the RMPSC method. The proposed DOB and RMPSC are determined by a multiple LMI-based optimization approach. Furthermore, parameter uncertainty within a certain range, due to manufacturing errors or aging deterioration, is considered and a systematic tuning method is proposed to obtain the optimal gains. Finally, an offline optimization method is developed that ensures a low computational load to enable real-time processing. Simulation results demonstrate the effectiveness and validity of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper discusses the dissipative filtering problem for discrete-time nonlinear networked systems with dynamic quantization and data packet dropouts. The Takagi–Sugeno (T–S) fuzzy model is employed to approximate the considered nonlinear plant. Both the measurement and performance outputs are assumed to be quantized by the dynamic quantizers before being transmitted. Moreover, the Bernoulli stochastic variables are utilized to characterize the effects of data packet dropouts on the measurement and performance outputs. The purpose of this paper is to design full- and reduced-order filters, such that the stochastic stability and dissipative filtering performance for the filtering error system can be guaranteed. The collaborative design conditions for the desired filter and the dynamic quantizers are expressed in the form of linear matrix inequalities. Finally, simulation results are used to illustrate the feasibility of the proposed filtering scheme. [ABSTRACT FROM AUTHOR]

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control systems with bounded disturbances. By constructing an appropriate Lyapunov–Krasovskii functional, we obtain a delay-dependent condition, which determines the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in the form of liner matrix inequalities is given to solve the problem of controller design and reachable set estimation. Then, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to show the effectiveness of our result. [ABSTRACT FROM AUTHOR]

Proposing a matrix transform method to solve a fractional partial differential equation is the main aim of this paper. The main model can be transferred to a partial-integro differential equation (PIDE) with a weakly singular kernel. The spatial direction is approximated by a fourth-order difference scheme. Also, the temporal derivative is discretized via a second-order numerical procedure. First, the spatial derivatives are approximated by a fourth-order operator to compute the second-order derivatives. This process produces a system of differential equations related to the time variable. Then, the Crank–Nicolson idea is utilized to achieve a full-discrete scheme. The kernel of the integral term is discretized by using the Lagrange polynomials to overcome its singularity. Subsequently, we prove the convergence and stability of the new difference scheme by utilizing the Rayleigh–Ritz theorem. Finally, some numerical examples in one-dimensional and two-dimensional cases are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper regards the outer synchronization of multi-layer dynamical networks with additive couplings via aperiodically intermittent pinning control, in which different layers of each multi-layer network have different topological structures. First, a state-feedback intermittent pinning controller is designed in the drive and response configuration, and sufficient conditions to achieve the outer synchronization are derived based on the Lyapunov stability theory and matrix inequalities. Second, outer synchronization problem of multi-layer networks is discussed by setting an adaptive intermittent pinning controller; an appropriate Lyapunov function is selected to prove the criteria of synchronization between the drive multi-layer network and the response multi-layer network. Finally, three simulation examples are given to show the effectiveness of our control schemes. [ABSTRACT FROM AUTHOR]

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS. [ABSTRACT FROM AUTHOR]

This paper presents a comfort-oriented semi-active suspension system composed of a network-synthesized passive section and a controllable section based on a semi-active inerter. Firstly, the semi-active suspension system is divided into a passive part and a controllable part. For the passive part, first-order and second-order robust positive real controllers are designed. The problem with H 2 cost is considered, and the bilinear matrix inequalities (BMI) are solved using an iterative method to obtain two admittance functions. The admittance functions are physically realized as two mechanical networks composed of mechanical passive elements such as inerter, spring, and damper (ISD). Then, the parameters of these mechanical elements in those networks are optimized by Particle Swarm Optimization (PSO). Secondly, a semi-active inerter based on Sky-hook control is introduced for the semi-active part of the suspension system. Finally, the semi-active ISD suspension structure is verified by a quarter vehicle model. The simulation results show that the first-order and second-order suspension systems optimize the RMS of the spring mass acceleration by 14.2% and 23.9%, respectively, as compared to traditional suspension systems. Furthermore, frequency-domain analysis also shows that both suspension systems effectively reduce the value of spring mass acceleration in the low-frequency band. [ABSTRACT FROM AUTHOR]

This work focuses on the design of a unified control law, which enhances the accuracy of both the disturbance estimation and stabilization of nonlinear T-S fuzzy semi-Markovian jump systems. In detail, a proportional-integral observer based equivalent-input-disturbance (PIO-EID) approach is considered to model and develop the controller. The PIO approach includes a variable for relaxation in the system design along with an additional term for integration to improve the flexibility of the design and endurance of the system. The proposed stability criteria are formulated in the form of matrix inequalities using Lyapunov theory and depend on the sojourn time for robust control design. Final analyses are performed using MATLAB software with simulations to endorse the theoretical findings of this paper. [ABSTRACT FROM AUTHOR]

In this paper, the stability problem for the digital redesign of discrete-time switched systems using H∞ linear matrix inequality (LMI) is investigated. We propose the switching time approach for digital redesign between controller work and failure, and this switching time will limit the system output within the system capacity. When the controller fails, the overall system will be unstable. Therefore, if the digital redesign controller is not restored in a certain period of time, the system output will exceed the system capacity. To solve this problem, we propose a switching law to determine the switching time between the stable mode (controller work) and the unstable (controller failure) mode; this will limit the overall system states in the unstable mode. In addition, the digital redesign controller has the advantage of faster tracking. After we propose a discrete-time switching system with stable and unstable modes, we use H∞ linear matrix inequality (LMI) and Lyapunov functions to prove the stability in detail. Finally, the numerical example illustrates the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a solution to the consensus problem for a particular category of uncertain switched multi-agent systems (MASs). In these systems, the communication topologies between agents and the system dynamics are governed by a time-homogeneous Markovian chain in a stochastic manner. To address this issue, we propose a novel neuroadaptive distributed dynamic event-triggered control (DETC) strategy. By leveraging stochastic Lyapunov theory and matrix inequality methodology, we establish sufficient conditions for practical ultimate mean square consensus (UMSBC) of MASs using a combination of neural networks (NNs) adaptive control strategy and DETC method. Our approach employs a distributed adaptive NNs DETC mechanism in MASs with unknown nonlinear dynamics and upgrades it at the moment of event sampling in an aperiodic manner, resulting in significant savings in computation and resources. We also exclude the Zeno phenomenon. Finally, we provide numerical examples to demonstrate the feasibility of our proposed approach, which outperforms existing approaches. [ABSTRACT FROM AUTHOR]

Diffusion is an inevitable important factor in advertising dynamic systems. However, previous literature did not involve this important diffusion factor, and only involved the local stability of the advertising model. This paper develops a global stability criterion for the impulsive advertising dynamic model with a feedback term under the influence of diffusion. Since global stability requires the unique existence of equilibrium points, variational methods are employed to solve it in the infinite dimensional function space, and then a global stability criterion of the system is derived by way of the impulse inequality lemma and orthogonal decomposition of a class of Sobolev spaces. Numerical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article is concerned with the adaptive-event-triggered filtering problem as it relates to a class of nonlinear discrete-time systems characterized by interval Type-2 fuzzy models. The system under investigation is susceptible to Markovian switching and deception attacks. It is proposed to implement an improved event-triggering mechanism to reduce the unnecessary signal transmissions on the communication channel and formulate the extended dissipativity specification to quantify the transient dynamics of filtering errors. By resorting to the linear matrix inequality approach and using the information on upper and lower membership functions, stochastic analysis establishes sufficient conditions for the existence of the desired filter, ensuring the mean-squared stability and extended dissipativity of the augmented filtering system. Further, an optimization-based algorithm (PSO) is proposed for computing filter gains at an optimal level of performance. The developed scheme was finally tested through experimental numerical illustrations based on a single-link robot arm and a lower limbs system. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Axioms titled "Optimisation Models and Applications." It explores the use of optimization models in various fields such as engineering, economics, health, and more. The issue includes several research papers that address different optimization problems and propose solutions using various algorithms and techniques. The papers cover topics such as control systems, traffic networks, image communication, sit-to-stand motion, and more. The authors of the papers have contributed equally to the writing, editing, and reviewing process. The document concludes with acknowledgments to the authors, reviewers, and editorial board, and declares no conflicts of interest. [Extracted from the article]

This study explores the synchronization issue for uncertain multi-link complex networks incorporating stochastic characteristics and hybrid delays. Unlike previous works, internal delays, coupling delays, and stochastic delays considered in our model change over time; meanwhile, the impulse strength and position change with time evolution. To actualize network synchronization, a strategy called hybrid impulsive pinning control is applied, which combines the virtue of impulsive control and pinning control as well as two categories of impulses (i.e., synchronization and desynchronization). By decomposing the complicated topological structures into diagonal items and off-diagonal items, multiple nonlinear coupling terms are linearly decomposed in the process of theoretical analysis. Combining inequality technology and matrix decomposition theory, several novel synchronization criteria have been gained to ensure synchronization for the concerning multi-link model. The criteria get in touch with the uncertain strengths, coupling strengths, hybrid impulse strengths, delay sizes, impulsive intervals, and network topologies. [ABSTRACT FROM AUTHOR]

The μ -value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness and performance of time-invariant systems. We establish and analyze new results concerning structured singular values for the Hadamard product of real square M-matrices. The new results are obtained for structured singular values while considering a set of block diagonal uncertainties. The targeted uncertainties are of two types, that is, pure real scalar block uncertainties and real full-block uncertainties. The eigenvalue perturbation result is utilized in order to determine the behavior of the spectrum of perturbed matrices (A ∘ B) Δ (t) and ((A ∘ B) T Δ (t) + Δ (t) (A ∘ B)) . [ABSTRACT FROM AUTHOR]

This research focuses on designing a min–max robust control based on a neural dynamic programming approach using a class of continuous differential neural networks (DNNs). The proposed controller solves the robust optimization of a proposed cost function that depends on the trajectories of a system with an uncertain mathematical model satisfying a class of non-linear perturbed systems. The dynamic programming min–max formulation enables robust control concerning bounded modelling uncertainties and disturbances. The Hamilton–Jacobi–Bellman (HJB) equation's value function, approximated by a DNN, permits to estimate the closed-loop formulation of the controller. The controller design is based on an estimated state trajectory with the worst possible uncertainties/perturbations that provide the degree of robustness using the proposed controller. The class of learning laws for the time-varying weights in the DNN is produced by studying the HJB partial differential equation. The controller uses the solution of the obtained learning laws and a time-varying Riccati equation. A recurrent algorithm based on the Kiefer–Wolfowitz method leads to adjusting the initial conditions for the weights to satisfy the final condition of the given cost function. The robust control suggested in this work is evaluated using a numerical example confirming the optimizing solution based on the DNN approximate for Bellman's value function. [ABSTRACT FROM AUTHOR]

This paper provides a procedure to design robust controllers based on observed states applied to three-phase inverters with LCL filters connected to a grid with uncertain and possibly time-varying impedances, which can arise in renewable energy systems and microgrid applications. Linear matrix inequalities are used to rapidly compute, off-line, based only on the choice of two scalar parameters for pole location, sets of gains for the controller and the observer, and also to provide a theoretical certificate of the closed-loop stability, including a limit for the rate of variations of the grid impedances. The proposed design procedure allows the easy implementation of robust state feedback controllers with a reduced number of sensors, ensuring good performance for different sets of grid impedances. Additionally, larger regions of guaranteed stability are provided by the proposed procedure, when compared with a similar condition from the literature. The control law using the observed states can ensure grid currents with low harmonic content, complying with the IEEE 1547 Standard requirements, with negligible loss of performance concerning the feedback of the measured state variables. Three optimal state feedback controllers from the literature are reproduced here and successfully implemented using the observed state variables based on the proposed procedure. In all cases, the viability of the proposal was confirmed by simulations and experimental results. [ABSTRACT FROM AUTHOR]

The problem of finite-time static output feedback H ∞ control for a class of discrete-time singular Markov jump systems is studied in this paper. With the consideration of network transmission delay and event-triggered schemes, a closed-loop model of a discrete-time singular Markov jump system is established under the static output feedback control law, and the corresponding sufficient condition is given to guarantee this system will be regular, causal, finite-time bounded and satisfy the given H ∞ performance. Based on the matrix decomposition algorithm, the output feedback controller can be reduced to a feasible solution of a set of strict matrix inequalities. A numerical example is presented to show the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

This study outlines the necessary and sufficient criteria for swarm stability asymptotically, meaning consensus in a class of fractional-order multi-agent systems (FOMAS) with interval uncertainties for both fractional orders 0 < α < 1 and 1 < α < 2. The constraints are determined by the graph topology, agent dynamics, and neighbor interactions. It is demonstrated that the fractional-order interval multi-agent system achieves consensus if and only if there are some Hermitian matrices that satisfy a particular kind of complex Lyapunov inequality for all of the system vertex matrices. This is done by using the existence condition of the Hermitian matrices in a Lyapunov inequality. To do this, at first it is shown under which conditions a multi-agent system with unstable agents can still achieve consensus. Then, using a lemma and a theory, the Lyapunov inequality regarding the negativity of the maximum eigenvalue of an augmented matrix of a FOMAS is used to find some Hermitian matrices by checking only a limited number of system vertex matrices. As a result, the necessary and sufficient conditions to reach consensus in a FOMAS in the presence of internal uncertainties are obtained according to the Lyapunov inequalities. Using the main theory of the current paper, instead of countless matrices, only a limited number of vertex matrices need to be used in Lyapunov inequalities to find some Hermitian matrices. As a confirmation of the notion, some instances from numerical simulation are also provided at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, the formation coordination control of discrete-time distributed leaderless multiple autonomous underwater vehicle (AUV) system with double independent position–velocity communication topology and control inputs on a nonconvex set is studied. Firstly, the problem of formation coordination control of multi-AUV system is transformed into the problem of formation consensus of multi-AUV system, and the consistent state of leaderless multi-AUV system formation was defined. Secondly, considering the existence of bounded communication delay and nonconvex control input constraints for multi-AUV system formation under weak communication conditions, a formation consistent constraint controller algorithm for discrete-time leaderless multi-AUV system with double independent communication topology is proposed by introducing constraint operators. By using the properties of graph theory, random matrix and SIA matrix, and selecting appropriate controller parameters, the multi-AUV system formation can reach the defined consensus state. Furthermore, the unbounded communication delay of multi-AUV system formation is studied. Finally, the simulation results show that the proposed controller constraint algorithm is effective. [ABSTRACT FROM AUTHOR]

The paper deals with a robust sensor fault estimation by proposing a novel algorithm capable of reconstructing faults occurring in the system. The provided approach relies on calculating the fault estimation adaptively in every discrete time instance. The approach is developed for the systems influenced by unknown measurement and process disturbance. Such an issue has been handled with applying the commonly known H ∞ approach. The novelty of the proposed algorithm consists of eliminating a difference between consecutive samples of the fault in an estimation error. This results in a easier way of designing the robust estimator by simplification of the linear matrix inequalities. The final part of the paper is devoted to an illustrative example with implementation to a laboratory two-rotor aerodynamical system. [ABSTRACT FROM AUTHOR]

This paper aims to investigate and categorize all inequivalent and irreducible Z + -modules of a commutative unit Z + -ring A , equipped with set {1, x, y, x y } satisfying x 2 = 1 , y 2 = 1 as a Z + -basis by using matrix equations, which was part of a call for a Special Issue about matrix inequalities and equations by Symmetry. If the rank of the Z + -module n ≤ 2 , we prove that there are finitely many inequivalent and irreducible Z + -modules, respectively, one and three. However, if n ≥ 3 , there is no irreducible Z + -module. [ABSTRACT FROM AUTHOR]

This paper considers the positivity-preserving model reduction for discrete-time positive systems. Given a stable high-order positive system, we aim to find a reduced-order model such that the approximation error is minimized within a prescribed H ∞ performance and positivity is preserved. Regarding the bounded real lemma, the sufficient and necessary condition for the existence of a reduced-order model is established in terms of bilinear matrix inequality and convex semi-definite constraint, which ensures that the reduced-order system is positive and the resulted error system is stable and has an H ∞ performance level. Based on the inner-approximation strategy, we approximate the bilinear constraints with convex ones, under which an iterative procedure is provided to calculate the desired reduced-order model. Finally, an example is provided to demonstrate the effectiveness and potential benefits of the presented results. [ABSTRACT FROM AUTHOR]

This article mainly concentrates on the synchronization problem for a more general kind of the master–slave memristor-based neural networks with fractional derivative. By applying a continuous-frequency-distributed equivalent model tool, some new outcomes and sufficient conditions on the robust synchronization of the master–slave neural networks with uncertainty are proposed via linear matrix inequality (LMI). Finally, two memristive neural networks model with fractional derivatives are presented to validate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates an improved criterion to synthesize dissipative observer-based controllers for Markovian jump fuzzy systems under model uncertainties. Since fuzzy-basis functions include some immeasurable state variable or uncertain parameters, there are differences in the fuzzy-basis functions between controller and plant, which is a mismatched phenomenon. This work presents the first attempt for applying double-fuzzy summation-based Lyapunov functions for the observer-based control scheme of the Markov jump fuzzy system regarding the mismatched phenomenon. To be specific, the dissipative conditions are formulated in terms of uncertain parameterized bilinear matrix inequalities. Based on the improved relaxation techniques, a linear-matrix-inequality (LMI)-based algorithm is proposed in the framework of sequence linear programming matrix method. The obtained observer-based controller ensures that the closed-loop system is stochastically stable, and the dissipative performances produce less conservative results compared to preceding works via two numerical examples. [ABSTRACT FROM AUTHOR]

In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional–differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov's theory. Two application examples verify the analytic findings. [ABSTRACT FROM AUTHOR]

In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed problem into an approximate uncertain optimal control problem with arbitrary accuracy because the dimension of Haar basis tends to infinity. The relative convergence theorem is proved. An application to an optimal control problem with an uncertain heat equation is dealt with to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with the asymptotic synchronization of fractional-order complex dynamical networks with different structures and parameter uncertainties (FCDNDP). Firstly, the FCDNDP model is proposed by the Riemann–Liouville (R-L) fractional derivative. According to the property of fractional calculus and the Lyapunov direct method, an original controller is proposed to achieve the asymptotic synchronization of FCDNDP. Our controller is more adaptable and effective than those in other literature. Secondly, a sufficient condition is given for the asymptotic synchronization of FCDNDP based on the asymptotic stability theorem and the matrix inequality technique. Finally, the numerical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of the system, is presented. Second, the relationship between general finite-time mean square stability, finite-time stochastic stability, and quantitative mean square exponential stability is proposed. Subsequently, some sufficient conditions for the existence of state feedback and observer-based controllers are derived, and an algorithm is offered to solve the matrix inequalities resulting from quantitative mean square exponential stabilization. Finally, the effectiveness of the proposed results is illustrated with the numerical example and the practical example. [ABSTRACT FROM AUTHOR]

This paper proposes a linear matrix inequality (LMI)-based adaptive barrier global sliding mode control (ABGSMC) for uncertain systems with faulty actuators. The proposed approach is derived using a novel global nonlinear sliding surface to guarantee the global dynamic property and to ensure system stability and the occurrence of sliding in the presence of actuator faults. The optimal coefficients of the sliding surface are determined using the LMI method. The system's asymptotic stability is proven using Lyapunov theory. Additionally, an adaptive barrier function is considered to ensure the convergence of the output variables to a predefined locality of zero in a limited time, even where external disturbances and actuator faults are present. In order to decrease the steepness of the control action and mitigate the chattering phenomenon, the hyperbolic tangent function is employed instead of the signum function in the sliding mode control. The proposed method is validated using a simulation study of the Genesio's chaotic system. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time contractively bounded control issue for positive linear systems under H ∞ performance. The notion of H ∞ finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the H ∞ finite-time contractive boundedness of the considered positive systems. A state feedback finite-time contractively bounded controller design method is proposed. The corresponding sufficient condition for the existence of the desired controller is derived by using the Lyapunov function method and the matrix inequality technique. Moreover, a computable scheme for solving the controller gain is established by employing the cone complementary linearization approach. Finally, a numerical example and an application example about pest management are used to validate the effectiveness of proposed conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the event-triggered fault diagnosis (FD) problem for interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy networked systems. Firstly, an FD fuzzy filter is proposed by using IT2 T-S fuzzy theory to generate a residual signal. This means that the FD filter premise variable needs to not be identical to the nonlinear networked systems (NNSs). The evaluation functions are referenced to determine the occurrence of system faults. Secondly, under the event-triggered mechanism, a fault residual system (FRS) is established with parameter uncertainty, external disturbance and time delay, which can reduce signal transmission and communication pressure. Thirdly, the progressive stability of the fault residual system is guaranteed by using the Lyapunov theory. For the energy bounded condition of external noise interference, the performance criterion is established using linear matrix inequalities. The matrix parameters of the target FD filter are obtained by the convex optimization method. A less conservative fault diagnosis method can be obtained. Finally, the simulation example is provided to illustrate the effectiveness and the practicalities of the proposed theoretical method. [ABSTRACT FROM AUTHOR]

This work investigates sensor fault diagnostics and fault-tolerant control for a voltage source converter based microgrid (model) using a sliding-mode observer. It aims to provide a diagnosis of multiple faults (i.e., magnitude, phase, and harmonics) occurring simultaneously or individually in current/potential transformers. A modified algorithm based on convex optimization is used to determine the gains of the sliding-mode observer, which utilizes the feasibility optimization or trace minimization of a Ricatti equation-based modification of H-Infinity ( H ∞ ) constrained linear matrix inequalities. The fault and disturbance estimation method is modified and improved with some corrections in previous works. The stability and finite-time reachability of the observers are also presented for the considered faulty and perturbed microgrid system. A proportional-integral (PI) based control is utilized for the conventional regulations required for frequency and voltage sags occurring in a microgrid. However, the same control block features fault-tolerant control (FTC) functionality. It is attained by incorporating a sliding-mode observer to reconstruct the faults of sensors (transformers), which are fed to the control block after correction. Simulation-based analysis is performed by presenting the results of state/output estimation, state/output estimation errors, fault reconstruction, estimated disturbances, and fault-tolerant control performance. Simulations are performed for sinusoidal, constant, linearly increasing, intermittent, sawtooth, and random sort of often occurring sensor faults. However, this paper includes results for the sinusoidal nature voltage/current sensor (transformer) fault and a linearly increasing type of fault, whereas the remaining results are part of the supplementary data file. The comparison analysis is performed in terms of observer gains being estimated by previously used techniques as compared to the proposed modified approach. It also includes the comparison of the voltage-frequency control implemented with and without the incorporation of the used observer based fault estimation and corrections, in the control block. The faults here are considered for voltage/current sensor transformers, but the approach works for a wide range of sensors. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of event-triggered H ∞ asynchronous filtering for Markov jump nonlinear systems with varying delay and unknown probabilities. An event-triggered scheduling scheme is adopted to decrease the transmission rate of measured outputs. The devised filter is mode dependent and asynchronous with the original system, which is represented by a hidden Markov model (HMM). Both the probability information involved in the original system and the filter are assumed to be only partly available. Under this framework, via employing the Lyapunov–Krasovskii functional and matrix inequality transformation techniques, a sufficient condition is given and the filter is further devised to ensure that the resulting filtering error dynamic system is stochastically stable with a desired H ∞ disturbance attenuation performance. Lastly, the validity of the presented filter design scheme is verified through a numerical example. [ABSTRACT FROM AUTHOR]

This paper deals with a new robust control design for autonomous vehicles. The goal is to perform lane-keeping under various constraints, mainly unknown curvature and lateral wind force. To reach this goal, a new formulation of Parallel Distributed Compensation (PDC) law is given. The quadratic Lyapunov stability and stabilization conditions of the discrete-time Takagi–Sugeno (T-S) model representing the autonomous vehicles are discussed. Sufficient design conditions expressed in terms of strict Linear Matrix Inequalities (LMIs) extracted from the linearization of the Bilinear Matrix Inequalities (BMIs) are proposed. An illustrative example is provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H ∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H ∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers. [ABSTRACT FROM AUTHOR]

This paper describes a design scheme for terminal sliding mode controllers of certain types of non-linear dynamical systems. Two classes of such systems are considered: the dynamic behavior of the first class of systems is described by non-linear second-order matrix differential equations, and the other class is described by non-linear first-order matrix differential equations. These two classes of non-linear systems are not completely disjointed, and are, therefore, investigated together; however, they are certainly not equivalent. In both cases, the systems experience unknown disturbances which are considered bounded. Sliding surfaces are defined by equations combining the state of the system and the expected trajectory. The control laws are drawn to force the system trajectory from an initial condition to the defined sliding surface in finite time. After reaching the sliding surface, the system trajectory remains on it. The effectiveness of the approaches proposed is verified by a few computer simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses the global outer synchronization problem between two fractional-order complex networks coupled in a drive-response configuration. In particular, for a given fractional-order complex network composed of Lur'e systems, an observer-type response network with non-fragile output feedback controllers is constructed. Both additive and multiplicative uncertainties that perturb the control gain matrices are considered. Then, using the stability theory of fractional-order systems and eigenvalue distribution of the Kronecker sum of matrices, we establish some sufficient conditions for global outer synchronization. Interestingly, the developed results are cast in the format of linear matrix inequalities (LMIs), which can be efficiently solved via the MATLAB LMI Control Toolbox. Finally, numerical simulations on fractional-order networks with nearest-neighbor and small-world topologies are given to support the theoretical analysis. [ABSTRACT FROM AUTHOR]