Delay-dependent stability criterion for discrete linear time-delay systems with state saturation nonlinearity

• Published in: Proceedings of the 31st Chinese Control Conference pp. 2559 - 2564
• Main Authors: Xiaofu Ji, Mingwei Ren, Zebin Yang
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-07-2012
• Subjects: Asymptotic stability; Discrete linear system; iterative linear matrix inequality; Linear matrix inequalities; Numerical stability; Stability criteria; State feedback; state saturation; Symmetric matrices; time delay; Vectors
• ISBN: 1467325813; 9781467325813
• ISSN: 1934-1768; 2161-2927

This paper is concerned with stability analysis for discrete linear time delay systems with state saturation nonlinearity. By introducing a free matrix whose infinity norm is less than or equal to 1, the discrete state under state saturation constraint is confined in a convex hull. In this way, a sufficient criterion for discrete linear time-delay systems with state saturation to be asymptotically stable is obtained in terms of bilinear matrix inequalities that can be solved using the presented iterative linear matrix inequality algorithm. The state feedback control law synthesis problem is also solved and the corresponding iterative linear matrix synthesis algorithm is given. Two numerical examples are used to show that the presented method is applicable and effective.