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The purpose of this paper is to provide a parametric description (parametrization) of all static output feedback stabilizing controllers for linear stochastic discrete‐time systems with Markovian switching, applications of this result to simultaneous and robust stabilization problems and obtaining of algorithms for computing stabilizing gains.

The proposed approach presents parameterization in terms of coupled linear matrix equations and quadratic matrix inequalities which depend on parameter matrices similar to weight matrices in linear quadratic regulator (LQR) theory. To avoid implementation problems, a convex approximation technique is used and linear matrix inequalities (LMI)‐based algorithms are obtained for computing of stabilizing gain.

The algorithms obtained in this paper are non‐iterative and used computationally efficient LMI technique. Moreover, it is possible to use well‐known LQR methodology in the process of controller design.

As a result of this paper, a new unified approach to design of static output feedback stabilizing control is developed. This approach leads to efficient stabilizing gain computation algorithms for both stochastic systems with Markovian switching and deterministic systems with polytopic uncertainty.

The aim of this paper is to address the problem of fault detection (FD) of linear continuous‐time multi‐agent systems.

A mixed H_∞/H₋ formulation of the FD problem using semi‐decentralized filters is presented.

It is shown that through a decomposition approach the drawbacks of the existing distributed FD design methods in multi‐agent systems can be effectively tackled. An extended linear matrix inequality (LMI) characterization is used to reduce the conservativeness of the design solution by introducing additional matrices in order to eliminate the couplings of the Lyapunov matrices with the agent's matrices.

It is shown that by applying the proposed decomposition approach the FD problem of multi‐agent systems can be solved by analyzing the problem of a set of decoupled systems whose order and complexity are equal to that of a single agent. This procedure will be useful for both simplifying the computational cost of the solution as well as for developing a fault detection filter having a semi‐decentralized architecture.

Application of this methodology to a network of micro‐air vehicles (MAVs) illustrates the effectiveness and capabilities of the proposed design methodology.

The feasibility of the use of reliable and self‐healing network of unmanned systems, cooperative networks, and multi‐agent systems will be significantly enhanced and improved by the development of advanced fault detection and isolation (FDI) technologies.

A semi‐decentralized fault detection (FD) methodology is developed for linear multi‐agent networked systems to reduce the order and complexity of the observers at each agent. A mixed H_∞/H₋ formulation of the FD problem by using semi‐decentralized filters is presented. Using this approach each agent can not only detect its own faults but also is able to detect its nearest neighbor agents’ faults.

The purpose of this paper is to develop a methodology for the stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

The authors perform Briat Lemma, multiple integral approach and linear convex combination technique to investigate a class of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay. New sufficient criterion is established by linear matrix inequalities conditions.

It turns out that the obtained methods are easy to be verified and result in less conservative conditions than the existing literature. Two examples show the effectiveness of the proposed results.

The novelty of the proposed approach lies in establishing a new Wirtinger-based integral inequality and the use of the Lyapunov functional method, Briat Lemma, multiple integral approach and linear convex combination technique for stochastically asymptotic stability of fuzzy Markovian jumping neural networks with time-varying delay and continuously distributed delay in mean square.

Nonlinear systems identification from experimental data without any prior knowledge of the system parameters is a challenge in control and process diagnostic. It determines mathematical model parameters that are able to reproduce the dynamic behavior of a system. This paper aims to combine two fundamental research areas: MIMO state space system identification and nonlinear control system. This combination produces a technique that leads to robust stabilization of a nonlinear Takagi–Sugeno fuzzy system (T-S).

The first part of this paper describes the identification based on the Numerical algorithm for Subspace State Space System IDentification (N4SID). The second part, from the identified models of first part, explains how we use the interpolation of linear time invariants models to build a nonlinear multiple model system, T-S model. For demonstration purposes, conditions on stability and stabilization of discrete time, T-S model were discussed.

Stability analysis based on the quadratic Lyapunov function to simplify implementation was explained in this paper. The linear matrix inequalities technique obtained from the linearization of the bilinear matrix inequalities was computed. The suggested N4SID2 algorithm had the smallest error value compared to other algorithms for all estimated system matrices.

The stabilization of the closed-loop discrete time T-S system, using the improved parallel distributed compensation control law, was discussed to reconstruct the state from nonlinear Luenberger observers.

The purpose of this paper is to develop a methodology for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

The authors perform drive-response concept and time-delay feedback control techniques to investigate a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. New sufficient criterion is established without strict conditions imposed on the activation functions.

It turns out that the approach results in new sufficient criterion easy to be verified but without the usual assumption of the differentiability and monotonicity of the activation functions. Two examples show the effectiveness of the obtained results.

The novelty of the proposed approach lies in removing the usual assumption of the differentiability and monotonicity of the activation functions, and the use of the Lyapunov functional method, Jensen integral inequality, a novel Gu’s lemma, reciprocal convex and linear convex combination technique for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

The purpose of this paper is to present the methodology to the robust stability analysis of a vision‐based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matrix inequality (LMI) optimization. The effectiveness of the proposed approach can be witnessed by applying it to two‐link robotic manipulator with the camera mounted on the end‐effector.

The objective of this research is the analysis of uncertain nonlinear system by representing it in differential‐algebraic form. By invoking the suitable system representation and Lyapunov analysis, the stability conditions are described in terms of linear matrix inequalities.

The proposed method is proved robust in the presence of parametric uncertainties.

Through a differential‐algebraic equation, LMI conditions are devised that ensure the stability of the uncertain system while providing an estimate of the domain of attraction based upon quadratic Lyapunov function.

The purpose of this paper is with delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

Based on linear matrix inequality and algebra Riccati matrix equation, the stabilization result is derived to guarantee asymptotically stable and applicated in chaos synchronization of Rössler chaotic system with multiple time-delays.

A controller is designed and added to the nonlinear system with multiple time-delays. The stability of the nonlinear system at its zero equilibrium point is guaranteed by applying the appropriate controller signal based on linear matrix inequality and algebra Riccati matrix equation scheme. Another effective controller is also designed for the global asymptotic synchronization on the Rössler system based on the structure of delay-independent stabilization of nonlinear systems with multiple time-delays. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme.

The introduced approach is interesting for delay-independent stabilization of nonlinear systems with multiple time-delays and its application in chaos synchronization of Rössler system.

This paper aims to study the issues of output reachable set estimation for the linear singular Markovian jump systems (SMJSs) with time-varying delay based on a proportional plus derivative (PD) bumpless transfer (BT) output feedback (OF) control scheme.

To begin with, a sufficient criterion is given in the form of a linear matrix inequality based on the Lyapunov stability theory. Then, a PD-BT OF controller is designed to keep all the output signs of the system are maintain within a predetermined ellipsoid. Finally, numerical and practical examples are used to demonstrate the efficiency of the approach.

Based on PD control and BT control method, an OF control strategy for the linear SMJSs with time-varying delay is proposed.

The output reachable set synthesis of linear SMJSs with time-varying delay can be solved by using the proposed approach. Besides, to obtain more general results, the restrictive assumptions of some parameters are removed. Furthermore, a sufficiently small ellipsoid can be obtained by the design scheme adopted in this paper, which reduces the conservatism of the existing results.

The purpose of this paper is to develop a method for the existence, uniqueness and globally robust stability of the equilibrium point for Cohen–Grossberg neural networks with time-varying delays, continuous distributed delays and a kind of discontinuous activation functions.

Based on the Leray–Schauder alternative theorem and chain rule, by using a novel integral inequality dealing with monotone non-decreasing function, the authors obtain a delay-dependent sufficient condition with less conservativeness for robust stability of considered neural networks.

It turns out that the authors’ delay-dependent sufficient condition can be formed in terms of linear matrix inequalities conditions. Two examples show the effectiveness of the obtained results.

The novelty of the proposed approach lies in dealing with a new kind of discontinuous activation functions by using the Leray–Schauder alternative theorem, chain rule and a novel integral inequality on monotone non-decreasing function.

This paper proposes a novel method of fault detection, which is based on H_/H∞ Runge–Kutta observer and an adaptive threshold for a class of closed-loop non-linear systems. The purpose of this paper is to improve the rapidity and accuracy of fault detection.

First, the authors design the H_/H∞ Runge–Kutta fault detection observer, which is used as a residual generator to decouple the residual from the input. The H_ performance index metric in the specified frequency domain is used to describe how sensitive the residual to the fault. The H∞ norm is used to describe the residual robustness to the external disturbance of the systems. The residual generator is designed to achieve the best tradeoff between robustness against unknown disturbances but sensitivity to faults, thus realizing the accurate detection of the fault by suppressing the influence of noise and disturbance on the residual. Next, the design of the H_/H∞ fault detection observer is transformed into a convex optimization problem and solved by linear matrix inequality. Then, a new adaptive threshold is designed to improve the accuracy of fault detection.

The effectiveness and correctness of the method are tested in simulation experiments.

This paper presents a novel approach to improve the accuracy and rapidity of fault detection for closed-loop non-linear system with disturbances and noise.