%0 Journal Article
%T Stability of Hybrid Stochastic Systems with Time-Delay
%A Pu Xing-cheng
%A Yuan Wei
%J ISRN Mathematical Analysis
%D 2014
%R 10.1155/2014/423413
%X This paper develops some criteria for a kind of hybrid stochastic systems with time-delay, which improve existing results on hybrid systems without considering noises. The improved results show that the presence of noise is quite involved in the stability analysis of hybrid systems. New results can be used to analyze the stability of a kind of stochastic hybrid impulsive and switching neural networks (SHISNN). Therefore, stability analysis of SHISNN can be turned into solving a linear matrix inequality (LMI). 1. Introduction With the development of social production, many practical systems cannot be modeled by linear time-invariant systems. In this case, hybrid systems are employed to model many practical systems. A hybrid system is a dynamical system with continuous dynamics, discrete dynamics, and the interaction between them (see, e.g., [1¨C3]). Hybrid systems are important from both the practical and theoretical point of view. In fact, hybrid systems naturally represent a wide class of practical systems which are subject to known or unknown abrupt parameter variations and which undergo sudden change of system structures due to the failure of a component. Another practical motivation for studying hybrid dynamical systems originates from the fact that the hybrid control scheme provides an effective approach for controlling highly nonlinear complex dynamical systems and systems with uncertain and/or unknown parameters. From theoretical viewpoints, the interactions between low-level continuous dynamics and high-level discrete logics, mainly governed by the switching and impulsive mechanisms, bring new challenges beyond the conventional system theory. An area of particular interest has been the analysis of stability of hybrid dynamical systems (see, e.g., [4¨C9]). Impulsive stabilization of dynamical systems has attracted increasing interests in fields such as population dynamics, automatic control, drug administration, and communication networks (see [4, 5, 8]) and references therein). In many cases, impulsive stabilization may give better performance than continuous stabilization since the former is implemented only at impulsive instants (see [10]) while the latter does so at every moment (see [5]). Even in some cases, only impulsive stabilization can be used for control purpose. For instance, a central bank cannot change its interest rate every day in order to regulate the money supply in a financial market. The fundamental theoretic and systemic method of impulsive dynamical systems have been established in the recent years (see [1, 5]). On the other
%U http://www.hindawi.com/journals/isrn.mathematical.analysis/2014/423413/