Switched controller design for stabilization of nonlinear hybrid systems with time-varying delays in state and control.

*(English)*Zbl 1298.93290Summary: This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov-Krasovskii functional combined with Newton-Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.

##### MSC:

93D21 | Adaptive or robust stabilization |

93C73 | Perturbations in control/observation systems |

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |

##### Keywords:

switched controller; time-varying delay; stabilization; nonlinear perturbation; Riccati equation
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\textit{V. N. Phat}, J. Franklin Inst. 347, No. 1, 195--207 (2010; Zbl 1298.93290)

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