Grienggrai Rajchakit

Robust stability and stabilization of uncertain switched discrete-time systems

This paper is concerned with the robust stability and stabilization for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability and stabilization of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability and stabilization have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method, and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

Improved exponential convergence result for generalized neural networks including interval time-varying delayed signals

This article examines the exponential stability analysis problem of generalized neural networks (GNNs) including interval time-varying delayed states. A new improved exponential stability criterion is presented by establishing a proper Lyapunov-Krasovskii functional (LKF) and employing new analysis theory. The improved reciprocally convex combination (RCC) and weighted integral inequality (WII) techniques are utilized to obtain new sufficient conditions to ascertain the exponential stability result of such delayed GNNs. The superiority of the obtained results is clearly demonstrated by numerical examples.

New Results on Robust Stability and Stabilization of Linear Discrete-Time Stochastic Systems with Convex Polytopic Uncertainties

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of linear discrete-time stochastic control systems is given. Numerical examples are included to illustrate the effectiveness of our results.

A switching rule for exponential stability of switched recurrent neural networks with interval time-varying delay

This paper studies the problem for exponential stability of switched recurrent neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessarily differentiable. By constructing a set of argumented Lyapunov-Krasovskii functionals combined with the Newton-Leibniz formula, a switching rule for exponential stability of switched recurrent neural networks with interval time-varying delay is designed via linear matrix inequalities, and new sufficient conditions for the exponential stability of switched recurrent neural networks with interval time-varying delay via linear matrix inequalities (LMIs) are derived. A numerical example is given to illustrate the effectiveness of the obtained result.

Mean square robust stability of stochastic switched discrete-time systems with convex polytopic uncertainties

This article is concerned with mean square robust stability of stochastic switched discrete time-delay systems with convex polytopic uncertainties. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the mean square robust stability for the stochastic switched system with convex polytopic uncertainties is designed via linear matrix inequalities. Numerical examples are included to illustrate the effectiveness of the results.

Exponential stability of semi-Markovian jump generalized neural networks with interval time-varying delays

This draft addresses the exponential stability problem for semi-Markovian jump generalized neural networks (S-MJGNNs) with interval time-varying delays. The exponential stability conditions are derived by establishing a suitable Lyapunov–Krasovskii functional and applying new analysis method. Improved results are obtained to guarantee the exponential stability of S-MJGNNs through improved reciprocally convex combination and new weighted integral inequality techniques. The method in this paper shows the advantages over some existing ones. To verify the advantages and benefits of employing proposed method is explained through numerical examples.

Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay

This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen’s inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

Impulsive Cohen–Grossberg BAM neural networks with mixed time-delays: An exponential stability analysis issue

Abstract This paper investigates, the globally exponential stability analysis problem for a class of markovian jumping Cohen–Grossberg BAM-type neural networks (CGBAMNNs) with mixed time delays and impulsive effects. Here the jumping parameters are considered, which are governed by a markov process with discrete & finite state space. The mixed time delays carries both discrete time-varying and distributed delays, which means the lower and upper bounds of discrete time delays are available. By fabricating an appropriate Lyapunov–Krasovskii functional (LKF), some new sufficient conditions are obtained in terms of linear matrix inequalities (LMIs) to guarantee the globally exponential stability for the labeled neural networks. The obtained conditions are expressed in terms of LMIs whose feasibility can be checked easily by MATLAB LMI control toolbox. Furthermore, we have collated our effort with foregoing one in the available literatures and showed that it is less conserved. Finally, three numerical examples with their simulative reactions are provided to demonstrate the viability of the notional outcomes.

LMI approach to robust stability and stabilization of nonlinear uncertain discrete-time systems with convex polytopic uncertainties

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results.MSC:15A09, 52A10, 74M05, 93D05.