Positivity and decentralized L1 control of nonlinear interconnected switched positive systems under MDDT constraint

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

Nonlinear Analysis-Hybrid Systems Pub Date : 2023-08-17 DOI:10.1016/j.nahs.2023.101410

Shuo Li , Zilan Chen , Zhengrong Xiang

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引用次数: 0

Abstract

The article is focused on the problems of positivity and decentralized $L_{1}$ control for nonlinear interconnected switched positive systems(NISPSs) under mode-dependent dwell time(MDDT) constraint, which includes mode-dependent constant dwell time(MDCDT), mode-dependent minimum dwell time(MDMDT) and mode-dependent ranged dwell time(MDRDT) constraints. Both nonlinear subsystems and nonlinear interconnections are included in the considered NISPSs. First, a sufficient and necessary condition of positivity is presented for NISPSs. Next, by applying a novel discretized linear copositive Lyapunov function method, a sufficient condition of exponential stability with $L_{1}$ -gain performance is provided for NISPSs under MDCDT, MDMDT and MDRDT constraints, respectively. Further, by applying the matrix decomposition technology to the decentralized controller gain matrix, an effective mode-dependent piece-wise design scheme of decentralized $L_{1}$ controller in the solvable linear programming(LP) form is proposed for NISPSs under MDCDT, MDMDT and MDRDT constraints, respectively. The proposed decentralized $L_{1}$ controller design scheme for NISPSs under MDDT constraint can be degenerated into the one in mode-independent constraint case accordingly. At last, four examples with comparisons are given to illustrate the importance and effectiveness of the obtained results.

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MDDT约束下非线性互联切换正系统的正性和分散L1控制

本文研究了非线性互联切换正系统（NISPS）在依赖模式的驻留时间（MDDT）约束下的正性和分散L1控制问题，包括依赖模式的恒定驻留时间（MDCDT）、依赖模式的最小驻留时间（MDMDT）和依赖模式的范围驻留时间（MDRDT）约束。非线性子系统和非线性互连都包含在所考虑的NISP中。首先，给出了NISPs为正的一个充分必要条件。其次，通过应用一种新的离散线性正李雅普诺夫函数方法，分别在MDCDT、MDMDT和MDRDT约束下，为NISPS提供了具有L1增益性能的指数稳定性的充分条件。此外，通过将矩阵分解技术应用于分散控制器增益矩阵，分别针对MDCDT、MDMDT和MDRDT约束下的NISPS，提出了一种可解线性规划形式的分散L1控制器的有效模式相关分段设计方案。所提出的用于MDDT约束下的NISPS的分散L1控制器设计方案可以相应地退化为模式无关约束情况下的方案。最后，通过四个实例的比较，说明了所得结果的重要性和有效性。

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

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.