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Delay-dependent stabilization of linear systems with time-varying state and input delays. (English) Zbl 1093.93024
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:
93D15 Stabilization of systems by feedback
93C23 Control/observation systems governed by functional-differential equations
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