JIMO
Lyapunov method for stability of descriptor second-order and high-order systems
Guoshan Zhang Peizhao Yu
Journal of Industrial & Management Optimization 2018, 14(2): 673-686 doi: 10.3934/jimo.2017068

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.

keywords: Stability Lyapunov equations second-order systems linear matrix inequality

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