摘要
多线性动态系统是具有多个线性过程的复杂动态系统,包括切换线性系统、线性微分包含、线性参数变化系统等多类在系统控制理论中受到广泛关注的系统框架.本文以连续时间多线性动态系统的性能分析为目标,以笔者近几年的相关工作为基础,简要综述一类建立在实矩阵组之上的谱分析方法,包括矩阵组谱坐标定义,等价矩阵测度刻画,基于分段二次诱导测度的估计理论和逼近算法.作为一个应用例子,考虑单输入鲁里叶系统的绝对稳定性,给出基于谱分析方法的判据.
Multilinear dynamical systems are complex dynamical systems with multiple linear processes,which include switched linear systems,linear differential inclusions and linear parameter-varying systems that have been well-studied in the systems and control societies.This survey article presents a timely integration of spectral analysis for performance estimate of continuous-time multilinear dynamical systems,including the introduction of spectral abscissas for real matrix set,equivalence characteristic via least common matrix measure,and estimate theory and approximation procedures based on piecewise quadratic induced measures.As an implication,we discuss the absolute stability of Lure systems,and present a matrix-measure-based criterion.
出处
《控制理论与应用》
EI
CAS
CSCD
北大核心
2014年第7期872-877,共6页
Control Theory & Applications
基金
国家重点基础研究"973"计划资助项目(2014CB845302)
国家自然科学基金资助项目(61273121
60925013)
关键词
多线性动态系统
性能分析
谱坐标
矩阵组公共测度
绝对稳定性
multilinear dynamical systems
performance analysis
matrix set measures
piecewise quadratic induced measures
absolute stability
