不确定离散切换系统鲁棒保性能控制器设计

Design of robust guaranteed cost controllers for uncertain discrete-time switched systems

对一类具有范数有界参数不确定性的离散切换系统和一个二次型性能指标,研究其鲁棒保性能状态反馈控制器的设计问题.利用切换Lyapunov函数方法和线性矩阵不等式技术,给出了鲁棒保性能控制器存在的一个充分条件,并获得了控制器的一个参数化表示.在此基础上,将次优保性能控制器的设计问题转化为基于线性矩阵不等式约束下的凸优化问题.数值例子说明了所提设计方法的有效性.

For a class of discrete-time switched systems with norm bounded parameter uncertainty and a quadratic cost index, the problem of designing a suboptimal guaranteed cost state feedback controller is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by using a switched Lyapunov function approach together with linear matrix inequality technique, and the parameterized representation of the controllers is given in terms of linear matrix inequalities. Based on that, the design problem of the suboptimal guaranteed cost controller is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach.