Asynchronous control for 2-D switched systems with mode-dependent average dwell time.

*(English)*Zbl 1371.93073Summary: This work is concerned with asynchronous control for a class of two-dimensional switched systems with mode-dependent average dwell time. The systems are formulated by the famous Fornasini-Marchesini local state-space model, and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems. By extending mode-dependent average dwell time with the switched quadratic Lyapunov functional approach, the stabilization condition is established for 2-D asynchronously switched systems. Based on the stabilization result, mode-dependent state-feedback controllers are designed to guarantee \(\mathcal{H}_\infty\) performance and asymptotic stability of the corresponding closed-loop system. Finally, two examples are provided to illustrate the effectiveness of the proposed design scheme.

##### MSC:

93B36 | \(H^\infty\)-control |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93D15 | Stabilization of systems by feedback |

93C55 | Discrete-time control/observation systems |

93C05 | Linear systems in control theory |

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

##### Keywords:

asynchronous switching; mode-dependent average dwell time; 2-D switching systems; \(\mathcal{H}_\infty\) control
Full Text:
DOI

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