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Zbl 1093.93024
Zhang, Xian-Ming; Wu, Min; She, Jin-Hua; He, Yong
Delay-dependent stabilization of linear systems with time-varying state and input delays. (English)
[J] Automatica 41, No. 8, 1405-1412 (2005). ISSN 0005-1098

Summary: 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: $$\dot x(t)= Ax(t)+ A_1x(t-h_1(t))+ B_1u(t)+ B_2u(t-h_2(t)) .$$ 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 $(A,B_1)$ nor $(A+A_1,B_1)$ is stabilizable.

MSC 2000:: *93D15 Stabilization of systems by feedback
93C23 Systems governed by functional-differential equations

Keywords: Input delays; State delays; Delay-dependent stability; Stabilization; Integral inequality; Linear matrix inequality (LMI)

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