Lur'e系统镇定问题的非线性控制器设计

Nonlinear Controller Design for Absolute Stabilization Control Problems*

中文关键词  非线性系统  Lur'e系统  镇定  线性矩阵不等式

英文关键词  nonlinear system  stabilization  Lur'e system  absolute stability  algebraic matrix inequality

中文摘要

      本文研究了用Lur'e多非线性系统描述的被控对象的镇定问题．把问题的可解性归结到特殊的多线性矩阵不等式的可解性．非线性状态反馈和输出反馈控制器的设计分别依赖于一个双线性和三个三线性矩阵不等式的解．给出了基于线性矩阵不等式的交替寻优算法的设汁步骤.

英文摘要

      This paper discusses the absolute stabilization problem for Lur'e systems with multiple nonlinear loops in terms of state-space approach. Solvability conditions are presented to design nonlinear controllers such that the closed-loop system is absolutely stable via the algebraic matrix inequality (AMI) approach. It is shown that feedback controllers exist if and only if a class of special multilinear matrix inequalities (MI.Mls) are solvable. Also, the AMI-based design method obtained in this paper is simplified so as to be computationally feasible and tractable. The approach can be generalized to deal with other problems such as H2,H∞ and dissipation control problem.