In this paper, we obtain an analytical Lyapunovbased stability conditions for scalar linear and nonlinear stochastic systems with discrete time-delay. The Lyapunov– Krasovskii and Lyapunov–Razumikhin methods are applied with techniques from stochastic calculus to obtain the regions of mean square asymptotic stability in the parameter space. Both delay-independent and delay-dependent stability c...

Two ecient and numerically stable methods for the computation of the largest p Lyapunov characteristic exponents of an n dimensional discrete dynamical systems are presented. The eciencies of the proposed methods are compared with the eciencies of other methods through an operation count, and illustrated with an example. Ó 2000 Elsevier Science Inc. All rights reserved.

For partitions of f1; : : : ; ng, the classes of P -matrices are de ned, unifying the classes of the real P -matrices and of the real positive de nite matrices. Lyapunov scalar stability of matrices is de ned and characterized, and it is shown also that every real Lyapunov -scalar stable matrix is a P -matrix. Implication relations between Lyapunov scalar stability and H-stability are discussed.

In this paper a class of singularly perturbed system of conservation laws is considered. The partial differential equations are equipped with boundary conditions which may be studied to derive the exponential stability. Lyapunov stability technique is used to derive sufficient conditions for the exponential stability of this system. A Lyapunov function in H-norm for a singularly perturbed syste...

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochas...

In this paper, we introduce Lyapunov measure to verify weak (a.e.) notions of stability for an invariant set of a nonlinear dynamical system. Using certain linear operators from Ergodic theory, we derive Lyapunov results to deduce a.e. stability. In order to highlight the linearity of our approach, we also provide explicit formulas for obtaining Lyapunov function and Lyapunov measure in terms o...

We study hybrid dynamic systems on time scales. Using Lyapunov-like functions , we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales. 1. Introduction. In this paper, we present some sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid d...

Most of the existing results on stochastic stability use a single Lyapunov function, but we shall instead use multiple Lyapunov functions in this paper. We shall establish the sufficient condition, in terms of multiple Lyapunov functions, for the asymptotic behaviours of solutions of stochastic differential delay equations. Moreover, from them follow many effective criteria on stochastic asympt...

We show that existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided an additional mild assumption is fulfilled. For UGAS infinite-dimensional systems with external disturbances we derive a novel ’integral’ construction of non-coercive Lipschitz continuous Lyapunov functions. F...

This paper presents a converse Lyapunov function theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of wellknown classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded timevarying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differ...