Detectability of linear stochastic impulsive systems with state-dependent noises

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-02-01 DOI:10.1016/j.sysconle.2024.105989

Shixian Luo , Xin Chen , Feiqi Deng , Yan Jiang

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引用次数: 0

Abstract

This paper focuses on the characterization of moment detectability and almost sure detectability for linear stochastic impulsive systems. The concepts and characterizations of the

2 p

th moment detectability and almost sure detectability are first introduced. Two expanded systems, the state-expanded stochastic system and the moment equation, are established by utilizing the generalized

H

-representation technique. A series of geometric and algebraic conditions for the

2 p

th moment detectability of the linear stochastic impulsive systems are established by analyzing the 2nd moment detectability of the state-expanded system and the complete detectability of the moment equation. Subsequently, by introducing a strictly positive-definite quasi-periodic composite polynomial Lyapunov candidate, almost sure detectability criteria are framed in terms of linear matrix inequalities, showing that almost sure detectability is less conservative than moment detectability. Finally, two numerical examples with comparisons are provided to illustrate the proposed theoretical results.

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本文主要研究线性随机脉冲系统的矩可探测性和几乎确定可探测性的特征。首先介绍了第 2 次矩可探测性和几乎确定可探测性的概念和特征。利用广义 H 表示技术建立了两个扩展系统，即状态扩展随机系统和矩方程。通过分析状态扩展系统的第 2 矩可探测性和矩方程的完全可探测性，为线性随机脉冲系统的第 2pth 矩可探测性建立了一系列几何和代数条件。随后，通过引入严格正有限准周期复合多项式 Lyapunov 候选方程，用线性矩阵不等式框定了几乎确定的可探测性准则，表明几乎确定的可探测性不如矩可探测性保守。最后，提供了两个数值示例并进行了比较，以说明所提出的理论结果。

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 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.