LYAPUNOV METHOD FOR STABILITY OF DESCRIPTOR SECOND-ORDER AND HIGH-ORDER SYSTEMS

摘要

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