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: [email protected]?(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.

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