New Delay-dependent Stability Criteria for Uncertain Stochastic Systems with

Abstract - In this paper, the problem of delay-dependent stability of uncertain stochastic systems with time-varying delay is considered. The uncertainties are assumed to be norm-bounded. Based on the Lyapunov stability theory, new delay-dependent stability criteria for the system are derived in terms of LMI(linear matrix inequality). Two numerical examples are given to show the effectiveness of proposed method.Key Words : Time-varying delays, Linear matrix inequalities, Lyapunov method, Stochastic systems.†교신저자, 정회원 denotes: 충북대학교 전기공학과 조교수E-mail : madwind@chungbuk.ac.kr*정 회 원 : 영남대학교 전기공학과 부교수**정 회 원 : 대구대학교 전자공학부 전임강사 접수일자 : 2009년 8월 18일 최종완료 : 2009년 10월 1일 1. Introduction Time-delays frequently occurred in many industrial systems such as chemical processes, network controled systems, large-scale systems, cellular neural networks, synchronization between two chaotic systems, and so on. It is well known delay-dependent stability criteria, which includes the information on the size of delays, are generally less conservative than delay-independent ones. Therefore, many attention has been paid to the stability analysis of systems with time-delays. For example, see [1-8] and references therein. On the other hand, the stability analysis of stochastic systems with delays have been investigated by many researches since stochastic modeling came to play an important role in many fields of science and engineering applications. In this field, an important index for chencking the conservatism of stability criteria is the maximum delay bound for guaranteeing the asymptotic stability for the concerned system. Li et al [1] studied a delay-dependent and parameter-dependent robust stability criterion for stochastic time-delay systems with polytopic uncertainties. Yang et al [2] improved the stability criteria by fractioning delay intervals. Yue and Won [3] proposed new stability criterion for time-delay stochastic system with nonlinear uncertainties by using the neutral model transformation. Chen et al [4] proposed new delay-dependent stability criteria for stochastic systems with multiple delays by using a descriptor model transformation of the system and by applying Moon's inequality for bounding cross terms. In Yan et al [7] and Zhang et al [8], free weighting matrices are employed to reduce the conservatism of stability criteria for stochastic system with time-varying delays. However, there are still room for further improvement to the stability criteria for stochastic systems with time-varying delays. In this paper, we propose new improved delay-dependent stability criteria for uncertain stochastic systems with time-varying delays. Additional stochastic perturbations are considered as two cases: 1) trace bounded and 2) linear function and norm-bounded. By constructing a suitable Lyapunov-Krasovskii functional and employing appropriate free weighting matrices, new delay-dependent stability criteria are derived in terms of LMIs which can be solved efficiently by using the interior-point algorithm [9]. To reduce the conservatism of stability criteria, the integral terms obtained by calculating the stochastic differential of Lyaponov-Krasovskii's functionals are divided into two terms with different free weighting matrices. Two numerical examples are given and compared with the very recent ones to show the effectiveness of the proposed method.Notation : 