Mean square stability of linear stochastic neutral‐type time‐delay systems with multiple delays. (19th November 2018)

• Record Type: Journal Article
• Authors: Li, Zhao‐Yan; Lam, James; Fang, Ru
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 2(2019)
• Page Start: 451
• Page End: 472
• Publication Date: 2018-11-19
• Subjects: augmented Lyapunov‐Krasovskii functional -- mean square stability -- multiple time delays -- neutral‐type time‐delay systems -- stochastic systems; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4400
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: This paper studies mean square exponential stability of linear stochastic neutral‐type time‐delay systems with multiple point delays by using an augmented Lyapunov‐Krasovskii functional (LKF) approach. To build a suitable augmented LKF, a method is proposed to find an augmented state vector whose elements are linearly independent. With the help of the linearly independent augmented state vector, the constructed LKF, and properties of the stochastic integral, sufficient delay‐dependent stability conditions expressed by linear matrix inequalities are established to guarantee the mean square exponential stability of the system. Differently from previous results where the difference operator associated with the system needs to satisfy a condition in terms of matrix norms, in the current paper, the difference operator only needs to satisfy a less restrictive condition in terms of matrix spectral radius. The effectiveness of the proposed approach is illustrated by two numerical examples.