一类离散时间线性切换系统的二次鲁棒镇定

针对一类具有范数有界时变不确定性的离散时间线性切换系统,研究了其二次稳定化状态反馈控制律的设计问题.利用多李亚普诺夫函数法推导了在任意切换下二次稳定化控制律存在的充分条件,该条件被进一步等价地表示成线性矩阵不等式的可解性问题.同时它的解提供了二次稳定化控制律的一个参数化表示.仿真结果验证了所提方法的有效性.

Quadratic Robust Stabilization of a Class of Discrete-time Linear Switched Systems

For a class of discrete-time linear switched systems with norm-bounded time-varying uncertainty, the problem of designing quadratic stabilizing state feedback controllers is investigated. The sufficient condition for existence of such controllers under arbitrary switching sequences is derived using multiple Lyapunov function technique. Furthermore, it is shown that this condition is equivalent to the solvability problem of a set of certain linear matrix inequalities (LMIs), which can be solved by the existing efficient convex optimization techniques. The solutions of the LMIs provide a parameterized representation of the quadratic stabilizing controllers. Finally, examples are given to illustrate the effectiveness of the proposed results.