## 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

### Software:

Optimization Toolbox; LMI toolbox
Full Text:

### References:

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