Relaxed delay-dependent exponential stability condition for a class of neural networks with polytopic uncertainties and distributed delays

The global robust exponential stability of a class of neural networks with polytopic uncertainties and distributed delays is investigated in this paper.Parameter-dependent Lypaunov-Krasovskii functionals and free-weighting matrices are employed to obtain sufficient condition that guarantee the robust global exponential stability of the equilibrium point of the considered neural networks.The derived sufficient condition is proposed in terms of a set of relaxed linear matrix inequalities (LMIs),which can be checked easily by recently developed algorithms solving LMIs.A numerical example is given to demonstrate the effectiveness of the proposed criteria.     

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

This paper studies the exponential stability problems of discrete‐time and continuous‐time impulsive positive switched systems with mixed (discrete and distributed) time‐varying delays, respectively. By constructing novel copositive Lyapunov‐Krasovskii functionals and using the average dwell time technique, delay‐dependent sufficient conditions for the solvability of considered problems are given in terms of fairly simple linear matrix inequalities. Compared with the most existing results, by introducing an extra real vector, restrictive conditions on derivative of the time‐varying delays (less than 1) are relaxed, thus the obtained improved stability criteria can deal with a wider class of continuous‐time positive switched systems with time‐varying delays. Finally, two simple examples are provided to verify the validity of theoretical results.     

Robust H∞ filtering for a class of Markovian jump systems with time‐varying delays based on delta operator approach

In this paper, the robust H_∞ filtering problem for a class of discrete Markovian jump systems with time‐varying delays and linear fractional uncertainties is investigated based on delta operator approach. Based on Lyapunov‐Krasovskii functional in delta domain, new delay‐dependent sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired jump H_∞ filter is given. The proposed method can unify some previous related continuous and discrete systems into the delta operator systems framework. Numerical examples are given to illustrate the effectiveness of the developed techniques. © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach

This paper is concerned with the problem of the globally asymptotically mean square stability for a class of delayed genetic regularity networks (GRNs) with both parameter uncertainties and stochastic disturbances, where the time delays are belong to given intervals and assumed to be time varying. Based on choosing an appropriate and novel Lyapunov functional, a “delay fractioning” approach that is different from the existing ones is introduced. By utilizing $It\hat{o}\hbox{'}s$ differential formula and using the linear matrix inequality (LMI) method, we derive a robust asymptotical stability criterion in mean square sense for uncertain GRNs with time-varying delays. All the stability conditions are given in terms of LMIs. One example and its simulation are provided to show the advantages of the obtained result.     

Robust H∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching

This paper is concerned with the problems of robust stochastic stabilization and robust H_∞ control for uncertain discrete‐time stochastic bilinear systems with Markovian switching. The parameter uncertainties are time‐varying norm‐bounded. For the robust stochastic stabilization problem, the purpose is the design of a state feedback controller which ensures the robust stochastic stability of the closed‐loop system irrespective of all admissible parameter uncertainties; while for the robust H_∞ control problem, in addition to the robust stochastic stability requirement, a prescribed level of disturbance attenuation is required to be achieved. Sufficient conditions for the solvability of these problems are obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, explicit expressions of the desired state feedback controllers are also given. An illustrative example is provided to show the effectiveness of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays

In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for discrete-time stochastic neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequalities (LMIs). Furthermore, when the parameter uncertainties appear in the discrete-time stochastic neural networks with time-varying delays, the delay-dependent robust dissipativity criteria are also presented. Two examples are given to show the effectiveness and less conservatism of the proposed criteria.     

Delay‐dependent Stability and Static Output Feedback Control of 2‐D Discrete Systems with Interval Time‐varying Delays

This paper is concerned with the problems of delay‐dependent stability and static output feedback (SOF) control of two‐dimensional (2‐D) discrete systems with interval time‐varying delays, which are described by the Fornasini‐Marchesini (FM) second model. The upper and lower bounds of delays are considered. Applying a new method of estimating the upper bound on the difference of Lyapunov function that does not ignore any terms, a new delay‐dependent stability criteria based on linear matrix inequalities (LMIs) is derived. Then, given the lower bounds of time‐varying delays, the maximum upper bounds in the above LMIs are obtained through computing a convex optimization problem. Based on the stability criteria, the SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). With the use of the slack variable technique, a sufficient LMI condition is proposed for the BMI. Moreover, the SOF gain can be solved by LMIs. Numerical examples show the effectiveness and advantages of our results.     

Exponential Stability and Stabilization for Quadratic Discrete‐Time Systems with Time Delay

In this note, we deal with the exponential stability and stabilization problems for quadratic discrete‐time systems with time delay. By using the quadratic Lyapunov function and a so called ‘Finsler's lemma', delay‐independent sufficient conditions for local stability and stabilization for quadratic discrete‐time systems with time delay are derived in terms of linear matrix inequalities (LMIs). Based on these sufficient conditions, iterative linear matrix inequality algorithms are proposed for maximizing the stability regions of the systems. Finally, two examples are given to illustrate the effectiveness of the methods presented in this paper.     

Fault detection for a class of discrete‐time nonlinear systems subject to network‐induced uncertainties

This paper addresses the problem of fault detection (FD) for discrete‐time systems with global Lipschitz conditions and network‐induced uncertainties. By utilizing Bernoulli stochastic variables and a switching signal, a unified measurement model is proposed to describe three kinds of network‐induced uncertainties, that is, access constraints, time delays, and packet dropouts. We aim to design a mode‐dependent fault detection filter (FDF) such that, for all external disturbances and the above uncertainties, the error between the residual and fault is made as small as possible. The addressed FD problem is then converted into an auxiliary H_∞ filtering problem for discrete‐time stochastic system with multiple time‐varying delays. By applying the Lyapunov‐Krasovskii approach, a sufficient condition for the existence of the FDF is derived in terms of certain linear matrix inequalities (LMI). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the results obtained. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society