严格正实线性多变量系统的鲁棒性分析及其输出反馈控制

Robustness analysis and output feedback control for strictly positive real linear MIMO systems

讨论一类线性不确定系统的鲁棒严格正实分析和控制问题,其中各不确定参数矩阵具有线性分式形式.分析了这类系统对所有容许不确定性严格正实的条件,并综合了使闭环内稳且严格正实的动态输出反馈控制器.通过适当地构造增广系统,将这类问题转化为确定系统的严格正实分析和设计,并按增广系统给出了这类不确定系统鲁棒严格正实的充分必要条件以及动态输出反馈鲁棒严格正实控制器的存在条件.

The problem of robustly strict positive real analysis and synthesis is addressed for linear time-invariant systems subjected to a class of parameter uncertainty which can be expressed in a linear fraction form. The conditions under which the uncertain system is strictly positive real for all admissible uncertainties are characterized. A dynamic output-feedback controller is designed to stabilize the uncertain systems and achieve the extended strict positive realness property for a given closed-loop transfer function. By constructing augmented systems, the robustly strict positive real analysis and design for the uncertain systems can be converted into the strictly positive real analysis and synthesis for the system without uncertainties. Based on the augmented systems, necessary and sufficient conditions are obtained for the uncertain systems to be robustly strict positive real. Conditions for the existence of the dynamic output-feedback robustly strict positive real controller are also derived.