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The exponential H ∞ stabilization of Takagi–Sugeno fuzzy neutral-type neural networks with reaction–diffusion is investigated. A simple condition taking the form of linear matrix inequalities is presented by using Lyapunov functional, slack matrices, and the loop-invariant property of matrix trace. With the feasible solutions to these inequalities, a weight learning rule is derived to guarantee exponential H ∞ stability of the considered neural network. Then, a new LMIs-based condition on the existence of the weight learning rule is obtained by employing a more complex Lyapunov functional and the Jensen integral inequality. Finally, two numerical examples are given to illustrate the validity and lower conservatism of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the issue of L 2 - L ∞ filtering for time-delay reaction–diffusion switched Hopfield networks. Our main focus is on the design of a Luenberger estimator so that the filtering-error system not only is exponentially stable in the absence of external disturbance, but also possesses a predefined L 2 - L ∞ disturbance rejection level under the zero initial condition. With the aid of Lyapunov–Krasovskii functionals, several integral inequalities, and in conjunction with the free-weight matrix technique, both delay-independent and dependent design strategies are developed, where the required gains can be acquired through the feasible solution of linear matrix inequalities. To demonstrate the applicability and lower conservatism of the present design strategies, an example with numerical comparison is provided. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of two-objec-tive filtering for Takagi–Sugeno fuzzy Hopfield neural networks with time-variant delay. The intention is to design a fuzzy filter subject to random occurring gain perturbations to make sure that the filtering-error system achieves a pre-defined H ∞ and L 2 - L ∞ disturbance attenuation level in mean square simultaneously. Without imposing any additional constraints on the differentiability of the time-delay function, a criterion of the mean-square H ∞ and L 2 - L ∞ performance analysis for the filtering-error system is derived by means of an augmented Lyapunov functional and the second-order Bessel–Legendre inequality. Then, a numerically tractable design scheme is developed for the desired non-fragile H ∞ and L 2 - L ∞ filter, where the gains are able to be determined by the solution of some linear matrix inequalities. At last, a numerical example with simulations is provided to illustrate the applicability and superiority of the present H ∞ and L 2 - L ∞ filtering method. [ABSTRACT FROM AUTHOR]

Summary: This article deals with the issue of input‐to‐state ℋ∞ stabilization for recurrent neural networks with delay and external disturbance. The goal is to design a suitable weight‐learning law to make the considered network input‐to‐state stable with a predefined ℒ2‐gain. Based on the solution of linear matrix inequalities, two schemes for the desired learning law are presented via using decay‐rate‐dependent and decay‐rate‐independent Lyapunov functionals, respectively. It is shown that, in the absence of external disturbance, the proposed learning law also guarantees the exponential stability of the network. To illustrate the applicability of the present weight‐learning law, two numerical examples with simulations are given. [ABSTRACT FROM AUTHOR]

Passive filtering of neural networks with time-invariant delay and quantized output is considered. A criterion on the passivity of a filtering error system is proposed by means of the Lyapunov–Krasovskii functional and the Bessel–Legendre inequality. Based on the criterion, a design approach for desired passive filters is developed in terms of the feasible solution of a set of linear matrix inequalities. Then, analyses and syntheses are extended to the time-variant delay situation using the reciprocally convex combination inequality. Finally, a numerical example with simulations is used to illustrate the applicability and reduced conservatism of the present passive filter design approaches. [ABSTRACT FROM AUTHOR]

This paper addresses the issue of finite-time boundedness for time-delay neural networks with external disturbances via weight learning. With the help of a group of inequalities and combining with the Lyapunov theory, weight learning rules are devised to ensure the neural networks to be finite-time bounded for the fixed connection weight matrix case and the fixed delayed connection weight matrix case, respectively. Sufficient conditions on the existence of the desired learning rules are presented in the form of linear matrix inequalities, which are easily verified by MATLAB software. It is shown that the proposed learning rules also guarantee the finite-time stability of the time-delay neural networks. Finally, a numerical example is employed to show the applicability of the devised weight learning rules. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of energy-to-peak consensus for a class of multi-agent systems with both stochastic disturbances and Markovian switching topologies. The objective is to design a control protocol in the form of dynamic output feedback, such that the multi-agent system reaches mean square consensus and has a prescribed energy-to-peak disturbance attenuation level. By using linear transformations, the problem is transformed into a standard energy-to-peak control problem. Then a new bounded real lemma is established. On the basis of this, an approach for the design of the control protocol is developed, by which the desired gain can be obtained via solving a number of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper considers the problem of non-fragile observer-based H ∞ control for stochastic time-delay systems. The controller and observer to be designed are assumed to have norm-bounded gain perturbations. By choosing an appropriate Lyapunov–Krasovskii functional and introducing a slack matrix variable, a less conservative delay-dependent condition of exponential stability in mean square is presented in the form of linear matrix inequalities (LMIs). A stochastic bounded real lemma is then established. On the basis of this, a new LMI-based approach is developed for designing non-fragile observer-based H ∞ controllers without imposing any constraints on the system matrices. Finally, two numerical examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed design approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of non-fragile reduced-order dynamic output feedbackcontrol for both continuous- and discrete-time switched systems with average dwell-time switching. First, Lyapunov conditions for the analysis of asymptotic stability and weightedperformance are presented. Then, sufficient conditions for the solvability of the problem of controller design are developed in terms of linear matrix inequalities. The design methods are suitable for general switched systems, without the need to impose extra constraints on the system matrices. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This article deals with the problem of passivity analysis for delayed reaction–diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]

• Consider event-triggered extended dissipativity control for uncertain semi-Markov switching systems with disturbances. • Develop a mode- and disturbance-dependent switched event-triggered mechanism. • Propose a criterion for stochastic stability and extended dissipativity. • Present a co-design of the feedback-gain and event-triggered matrices in the framework of linear matrix inequalities. This paper is concerned with event-triggered extended dissipativity stabilization of uncertain semi-Markov switching systems with external disturbances. The purpose is to ensure the stochastic stability and extended dissipativity of the semi-Markov switching systems via using event-triggered control. A mode- and disturbance-dependent switched event-triggered mechanism is devised to determine the triggered moments, which can further reduce the number of triggered events compared to some existing switched event-triggered mechanisms. On the basis of the proposed mechanism, a time- and mode-dependent piecewise-defined Lyapunov functional is constructed to establish a criterion for the stochastic stability and extended dissipativity. Subsequently, a co-design scheme for the needed feedback-gain and event-triggered matrices is presented using some equivalent transformations of matrix inequalities. Lastly, a DC motor model and a robotic arm model are utilized to illustrate the validity of the designed controller. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of robust static output feedback H ∞ control for linear systems with polytopic uncertainties. A new method is proposed for robust static output feedback H ∞ controller design. The proposed design method is applicable for general uncertain systems, without the need to impose any constraints on system matrices. The corresponding design conditions are presented in the form of linear matrix inequalities (LMIs). One of the advantages of the new method lies in its less conservatism. The proposed design method is also applicable to both continuous-time and discrete-time systems. The performance of the method is compared with other methods based on several examples. [ABSTRACT FROM AUTHOR]

• This paper proposes the dissipativity performance analysis method for networked system with event-triggered protocol, dynamic quantization and sensor fault. • The method of co-design of the dynamic quantization parameter, event-triggered protocol and the filter parameters is given by means of LMI technique to ensure the filtering error system is asymptotically stable and satisfies the dissipativity performance. • Different from the existing results, an effective adjustment method of dynamic quantization parameter for the faulty measurement output is presented in this paper. This paper investigates the reliable event-based dissipative filter design problem for networked system with quantization and sensor fault. The attention is focused on proposing an effective filtering design method for ensuring the resulting filtering error system is asymptotically stable and guarantees dissipativity performance. Firstly, the dissipativity performance analysis criterion is given to check whether the asymptotic stability and the dissipativity performance are satisfied. Then, based on this, the design method for dissipative filter is established in terms of the classical linear matrix inequality technique. Finally, two practical examples are used to illustrate the effectiveness and feasibility of the developed algorithm. [ABSTRACT FROM AUTHOR]

Abstract: In general, a system with time delay may have multiple stable delay intervals. Especially, a stable delay interval does not always contain zero. Asymptotically accurate stability conditions such as discretized Lyapunov–Krasovskii functional (DLF) method and sum-of-square (SOS) method are especially effective for such systems. In this article, a DLF-based method is proposed to estimate the maximal stable delay interval accurately without using bisection when one point in this interval is given. The method is formulated as a generalized eigenvalue problem (GEVP) of linear matrix inequalities (LMIs), and an accurate estimate may be reached by iteration either in a finite number of steps or asymptotically. The coupled differential–difference equation formulation is used to illustrate the method. However, the idea can be easily adapted to the traditional differential–difference equation setting. [Copyright &y& Elsevier]

• The reliable exponential H ∞ filtering of switched reaction-diffusion neural networks is studied. • An analysis result on the exponential H ∞ performance is presented. • A linear matrix inequalities-based design scheme for the desired Luenberger observer is proposed. In this paper, the reliable exponential H ∞ filtering issue is studied for switched reaction-diffusion neural networks subject to exterior interference. The purpose is to design a Luenberger observer to make sure that the filtering error system possesses a pre-defined exponential H ∞ interference-rejection level against possible sensor failures. An analysis result on the exponential H ∞ performance is presented by the use of a Lyapunov functional together with a few inequalities. On its basis, a linear matrix inequalities-based design scheme for the Luenberger observer is proposed by getting rid of the nonlinear terms composed of the Lyapunov matrix, the gain matrix, and an uncertainty matrix caused by the sensor failures. In the case when the factors of sensor failures and reaction-diffusion are not concerned, the design scheme is shown to be an improvement over an existing design scheme. Finally, two examples are given to demonstrate the applicability and reduced conservatism of the obtained results, respectively. [ABSTRACT FROM AUTHOR]