Lyapunov method for stability of descriptor second-order and high-order systems

Guoshan  Zhang; Peizhao Yu

doi:10.3934/jimo.2017068

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2018, Volume 14, Issue 2: 673-686. Doi: 10.3934/jimo.2017068

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Lyapunov method for stability of descriptor second-order and high-order systems

Guoshan Zhang^, and
Peizhao Yu

School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

* Corresponding author: zhanggs@tju.edu.cn.
* Corresponding author: zhanggs@tju.edu.cn.

Received: April 2016

Revised: August 2016

Early access: May 2017

Published: April 2018

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Abstract

In this study, the stability problem of descriptor second-order systems is considered. Lyapunov equations for stability of second-order systemsare established by using Lyapunov method. The existence of solutions for Lyapunov equations are discussed and linear matrixinequality condition for stability of second-order systems aregiven. Then, based on the feasible solutions of the linear matrixinequality, all parametric solutions of Lyapunov equations are derived.Furthermore, the results of Lyapunov equations and linear matrixinequality condition for stability of second-ordersystems are extended to high-order systems. Finally, illustratingexamples are provided to show the effectiveness of the proposed method.

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Mathematics Subject Classification: Primary: 93D05, 93D20; Secondary: 93C05.

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Figure 2. State responses of system (16)

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