不确定系统的鲁棒严格正实设计的LMI方法

考虑系数矩阵具有有界范数不确定性系统的鲁棒严格正实设计问题.定义了不确定系统的二次严格正实性,得到了用线性矩阵不等式表示的系统二次严格正实的充要条件,给出了基于状态反馈的不确定系统二次严格正实鲁棒优化控制器的设计方法.

Robust Strict Positive Realness Synthesis for Uncertainty Systems with LMI Approach

This paper is devoted to synthesizing a stabilizing feedback controller for a linear time invariant plant with norm bounded uncertain coefficient matrices so that the corresponding closed loop system is robustly strictly positive real. Quadratic strict positive real system is defined first. Necessary and sufficient conditions for the system to be quadratic strict positive real are then established. Finally, state space formulas for the state feedback controller are given in terms of solutions to linear matrix inequalities. The feasibility of the proposed method is confirmed by a numerical example.