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

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.