驻留时间下切换仿射系统的实用镇定：从多面体到p-范数李雅普诺夫函数
Practical Stabilization of Switched Affine Systems under Dwell Time: From Polytopic to p-Norm Lyapunov Functions
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中文总结 AI 辅助
本文针对切换仿射系统在驻留时间约束下，提出基于加权p-范数李雅普诺夫函数的两步构造方法，实现期望工作点的实用渐近稳定，并推广了二次李雅普诺夫方法。
中文摘要 AI 辅助
本文研究在驻留时间约束下，切换仿射系统围绕期望工作点（该点并非子系统的公共平衡点）的镇定问题。由于在此设定下渐近镇定通常无法实现，目标变为确保轨迹收敛到并保持在包含期望工作点的指定区域内。主要贡献是开发了基于李雅普诺夫的工具，以适应比二次李雅普诺夫函数所诱导区域更一般的目标区域。特别地，我们为一大类加权p-范数函数建立了构造性李雅普诺夫刻画，该刻画推广了经典二次李雅普诺夫等价性，并支撑了所提出的混合控制和驻留时间发展。聚焦于期望区域为多面体的情况，并基于现有李雅普诺夫方法，我们开发了一种构造性两步方法：从平均系统的多面体李雅普诺夫证书出发，为所有足够大的p生成光滑的加权p-范数李雅普诺夫函数。我们证明该扩展保证了期望工作点的实用渐近稳定性，并在最小驻留时间切换下产生一个由李雅普诺夫证书保证的不变区域。数值例子说明了所提方法的有效性。
英文摘要
This paper addresses the stabilization of switched affine systems under dwell-time constraints around a desired operating point that is not a common equilibrium of the subsystems. Since asymptotic stabilization is generally unattainable in this setting, the objective is to ensure that trajectories converge to and remain within a prescribed region containing the desired operating point. The main contribution is the development of Lyapunov-based tools that accommodate target regions more general than those induced by quadratic Lyapunov functions. In particular, we establish a constructive Lyapunov characterization for a broad family of weighted $p$-norm functions, which generalizes the classical quadratic Lyapunov equivalence and underpins the proposed hybrid-control and dwell-time developments. Focusing on the case in which the desired region is a polytope, and building on existing Lyapunov-based methods, we develop a constructive two-step method that starts from a polytopic Lyapunov certificate for the average system and yields a smooth weighted $p$-norm Lyapunov function for all sufficiently large $p$. We prove that this extension guarantees practical asymptotic stability of the desired operating point and yields a Lyapunov-certified invariant region under minimum dwell-time switching. Numerical examples illustrate the effectiveness of the proposed method.
发表机构
- Centro Internacional Franco-Argentino de Cs. de la Información y de Sistemas (CIFASIS), UNR–CONICET（中法阿根廷信息与系统国际中心（CIFASIS），罗萨里奥国立大学-国家科学研究委员会）
- Military Institute of Engineering（军事工程学院）
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