A Generalized Lyapunov Function for Liénard-Type Nonlinear System with First-order Lag Elements

摘要

In this paper, the direct method of Lyapunov is used to study the stability of a Liénard-type nonlinear system with first-order lag elements. To establish the procedure for constructing Lyapunov function, the system is rewritten by a transformation. Then, a stability criterion for the system, which introduces a new type Lyapunov function, is presented. While the positive matrix P appeared in the Lyapunov function is obtained by solving matrix equations, the possibility of existence of P is discussed from the point of view of the condition the Luré-type Lyapunov function for the well-known nonlinear feedback control systems exists.