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This paper addresses decentralized exponential stability problem for a class of nonlinear large-scale systems with time-varying delay in interconnection is considered. 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 LeibnizNewton’s formula, new delay-dependent sufficient conditions for the existence of decentralized exponential stability is established in terms of LMIs. AMS Subject Classification: 93C30, 93D20, 37C75, 34G20, 93A15

This paper addresses exponential stability problem for a class of stochastic hybrid systems with time-varying delay. 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, new delay-dependent sufficient conditions for exponential stability of stochastic hybrid systems with time-varying delay are first established in terms of LMIs.

This article is concerned with robust stability of 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 robust stability for switched system with convex polytopic uncertainties is designed via linear matrix inequalities. AMS Subject Classification: 47N10, 93C55, 93D20, 94C10

This paper studies the problem for exponential stability of switched neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of augmented Lyapunov-Krasovskii functional combined with Newton-Leibniz formula, a switching rule and switching design for exponential stability for 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). AMS Subject Classification: 92B05, 93D20

This paper is concerned with mean square exponential stability of stochastic systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, new delay-dependent sufficient conditions for the mean square exponential stability of the stochastic systems are first established in terms of LMIs. AMS Subject Classification: 15A09, 52A10, 74M05, 93D05

This paper studies the problem of guaranteed cost control for a class of Hopfield delayed neural networks. The time delay is a continuous func- tion belonging to a given interval, but not necessary to be differentiable. A cost function is considered as a nonlinear performance measure for the closed-loop system. The stabilizing controllers to be designed must satisfy some expo- nential stability constraints on the closed-loop poles. By constructing a set of augmented Lyapunov-Krasovskii functional combined with Newton-Leibniz formula, a guaranteed cost controller is designed via memoryless state feedback control and new sufficient conditions for the existence of theguaranteed cost state-feedback for the system are given in terms of linear matrix inequalities (LMIs).