Delay-dependent stabilization of linear systems with time-varying state and input delays

The Integral-Inequality Method is a new way of tackling the delay-dependent stabilization problem for a linear system with time-varying state and input delays: x(t) = Ax(t) + A1x(t - h1(t)) + B1u(t) + B2u(t - h2(t)). In this paper, a new integral inequality for quadratic terms is first established. Then, it is used to obtain a new state- and input-delay-dependent criterion that ensures the stability of the closed-loop system with a memoryless state feedback controller. Finally, some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective, even though neither (A, B1) nor (A + A1, B1) is stabilizable. Key words: input delays; state delays; delay-dependent stability; robust stabilization; integral inequality; linear matrix inequality (LMI).

• Type: Journal
• Year: 2005
• Where: AUTOMATICA
• Authors: Xian-Ming Zhang, Min Wu, Jin-Hua She, Yong He
• Keywords: AUTOMATICA 2005, Delay-dependent Stabilization Problem, Input Delays, Integral Inequality