不确定多时滞切换混杂系统的鲁棒控制器设计

Robust Controller Design of Uncertain Multi-delay Switched Hybrid Systems

讨论了一类不确定多时滞切换混杂系统在任意切换条件下鲁棒渐近稳定的问题,提出了在给定L2增益的情况下系统能够保持鲁棒渐近稳定的充分条件,并采用线性矩阵不等式的形式进行描述.利用公共李雅普诺夫方法研究了不确定多时滞切换混杂系统的鲁棒镇定问题,设计了状态反馈控制器,保证了具有给定L2增益的切换系统在任意切换条件下的鲁棒渐近稳定性质,通过算例验证了所提出方法的有效性.定理中的条件均由线性矩阵不等式得出,易于工程实现.

The problem of robustly asymptotic stability for a class of uncertain multi-delay switched hybrid systems is discussed on the arbitrarily switched condition. The sufficient condition that such a system can keep up its robustly asymptotic stability if the L2 gain is given is put forward, which is described by linear matrix inequality. The robust stabilization problem of switched hybrid system is studied by using common Lyapunov function and the state feedback controller is designed. The robustly asymptotic stability in this system with the known L2 gain is thus guaranteed on the arbitrarily switched condition. The validity of the method proposed is verified by numerical examples.