## State feedback stabilization of time-varying delay uncertain systems: A delay decomposition approach.(English)Zbl 1257.93076

Summary: This paper focuses on the problem of asymptotic stabilization for time-varying delay uncertain systems. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stabilization criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Based on this, a delay-dependent sufficient condition for the existence of a state feedback controller ensuring stability of the closed-loop dynamics is proposed. Then, based on the Lyapunov method, a delay-dependent stabilization criterion is devised by taking the relationship between terms in the Leibniz-Newton formula into account. Integral Inequality Approach (IIA) and delay decomposition approach are used to express this relationship and an LMIs-based algorithm to design the controller stabilizing the system.

### MSC:

 93D15 Stabilization of systems by feedback 93C41 Control/observation systems with incomplete information 93C15 Control/observation systems governed by ordinary differential equations 93B40 Computational methods in systems theory (MSC2010)
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### References:

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