gap度量下线性时变系统的最优鲁棒性  

Optimal robustness in the gap metric for LTV systems

作　　者：王佳月 于天秋 曹书豪 司娜 WANG Jiayue;YU Tianqiu;CAO Shuhao;SI Na(College of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2023年第6期654-662,共9页Journal of Natural Science of Heilongjiang University

基　　金：黑龙江省自然科学基金(LH2021A017)。

摘　　要：本文主要研究了离散时间线性时变(Linear time-varying,LTV)系统中基于gap度量的鲁棒性优化问题,该问题涉及最大稳定性边缘的计算。借助套代数中算子的内外因子分解方法,推导出了最大稳定性边缘的公式,并证明了一致渐近时不变LTV系统最优控制器的存在性。The problem of robustness optimization with respect to the gap metric in the context of discrete-time Linear time-varying(LTV)systems is considered,which involves the computation of the maximum stability margin.Based on the inner-outer factorization of operators in nest algebras,a formula for the maximum stability margin is derived.Furthermore,the existence of an optimal controller is proved for uniformly asymptotically time-invariant LTV systems.

关 键 词：最大稳定边缘 gap度量 线性时变系统 套代数 

分 类 号：O177.1[理学—数学]