Stability and stabilization of discrete-time linear time-varying systems via Lyapunov difference equations and inequalities

IF 2.5 3区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS
Jiacheng Dong, Bin Zhou
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引用次数: 0

Abstract

In this paper, the stability and stabilization issues of discrete-time linear time-varying (DLTV) systems are investigated. The recently proposed concepts of stability for continuous linear time-varying (LTV) systems are extended to DLTV systems, including uniform upper boundedness (by an exponential function) and uniform lower boundedness (by an exponential function). For the newly proposed concepts of stability, techniques for testing stability are developed. First, utilizing the scalar stable function, the Lyapunov difference inequalities (LDIs) provide both sufficient and necessary conditions for the new concepts of stability. Second, sufficient and necessary criteria based on Lyapunov difference equations are presented. Third, by introducing uniform complete controllability and uniform complete reconstructibility, the Lyapunov equations whose matrix Q is degenerated are further examined. Finally, a method for designing state feedback controller is presented.
离散线性时变系统的Lyapunov差分方程与不等式的稳定性与稳定化
本文研究了离散线性时变系统的稳定性和镇定问题。将最近提出的连续线性时变系统稳定性的概念推广到连续线性时变系统,包括一致上界性(由指数函数)和一致下界性(由指数函数)。针对新提出的稳定性概念,开发了稳定性测试技术。首先,利用标量稳定函数,Lyapunov差分不等式为稳定性的新概念提供了充分必要条件。其次,给出了基于Lyapunov差分方程的充分必要判据。第三,通过引入一致完全可控性和一致完全重构性,进一步研究了矩阵Q退化的Lyapunov方程。最后,提出了一种状态反馈控制器的设计方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Systems & Control Letters
Systems & Control Letters 工程技术-运筹学与管理科学
CiteScore
4.60
自引率
3.80%
发文量
144
审稿时长
6 months
期刊介绍: Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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