一大类具有周期性系数的离散-时间 Riccati 型方程稳定解存在的必要和充分条件

IF 3.7 2区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Nonlinear Analysis-Hybrid Systems Pub Date : 2024-03-28 DOI:10.1016/j.nahs.2024.101490

Vasile Drăgan , Ioan-Lucian Popa , Samir Aberkane , Vladimir Răsvan

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引用次数: 0

摘要

本文致力于研究在确定性和随机性框架下的若干线性二次型（LQ）控制问题中出现的一大类离散时间后向里卡蒂方程。我们考虑了周期性时变情况。我们为这类方程提出了名为稳定解的全局特殊解的存在性和唯一性条件。除稳定条件外，本文所推导的标准还基于离散时间周期线性方程的特征乘数的一些合适属性，这些乘数是利用给定方程的系数充分构建的。我们的结果包含了文献中已有的几个结果，作为特殊情况。

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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A necessary and sufficient condition for the existence of the stabilizing solution of a large class of discrete-time Riccati type equations with periodic coefficients

This paper is devoted to the study of a large class of discrete-time backward Riccati equations arising in several linear quadratic (LQ) type control problems both in the deterministic and in the stochastic frameworks. The periodic time-varying case is considered. We propose existence and uniqueness conditions for a global special solution named stabilizing solution for such equations. Beside the stabilizability condition, the criterion derived in this paper is expressed based on some suitable properties of the characteristic multipliers of a discrete-time, periodic linear equation adequately constructed using the coefficients of the given equation. Our result englobes, as particular cases, several existing results in the literature.

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来源期刊

Nonlinear Analysis-Hybrid Systems AUTOMATION & CONTROL SYSTEMS-MATHEMATICS, APPLIED

CiteScore

8.30

自引率

9.50%

发文量

审稿时长

>12 weeks

期刊介绍： Nonlinear Analysis: Hybrid Systems welcomes all important research and expository papers in any discipline. Papers that are principally concerned with the theory of hybrid systems should contain significant results indicating relevant applications. Papers that emphasize applications should consist of important real world models and illuminating techniques. Papers that interrelate various aspects of hybrid systems will be most welcome.