New LKF approach for non-weighted L2 gain of switched linear systems with delay

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-01-17 DOI:10.1016/j.cnsns.2025.108612

Yachun Yang , Xiaodi Li , Xinsong Yang

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引用次数: 0

Abstract

This paper focuses on observer-state feedback control for global asymptotic stabilization (GAS) with non-weighted

L_{2}

-gain of switched linear systems with delay. Two kinds of mode-pendent event-triggered control (ETCs) are proposed for both the observer and the controller: one can exclude the Zeno phenomenon and adjust the event intervals by tuning the parameters while the other cannot. An innovative approach is established to ensure the monotonic decrease of the Lyapunov–Krasovskii functional (LKF) at switching moments, which makes it easy to analyze non-weighted

L_{2}

-gain of switched time-delay systems without any conservative transformation. Four key conclusions are presented using linear matrix inequalities (LMIs) to show the respective merits of the two ETC schemes. Two effective algorithms are presented to design the observer gains, the triggering weights, the control gains, and the minimum

L_{2}

-gains. Numerical simulations are employed to demonstrate the low conservatism and the merits of the obtained results.

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带延迟切换线性系统非加权增益的LKF新方法

研究了时滞切换线性系统非加权l2增益全局渐近镇定的观测器-状态反馈控制问题。针对观测器和控制器提出了两种模式相关的事件触发控制（ETCs）：一种可以排除芝诺现象并通过调整参数来调整事件间隔，而另一种则不能。提出了一种保证切换时刻Lyapunov-Krasovskii泛函（LKF）单调减小的创新方法，使得切换时滞系统的非加权l2增益分析不需要任何保守变换。利用线性矩阵不等式（lmi）给出了四个关键结论，以显示两种ETC方案各自的优点。提出了两种有效的算法来设计观测器增益、触发权值、控制增益和最小l2增益。数值模拟结果表明，该方法具有较低的保守性和较好的计算结果。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.