A Generalized Lyapunov Function For Lienard-Type Nonlinear Systems

H. Miyagi; K. Yamashita

doi:10.1117/12.942972

19 October 1987 A Generalized Lyapunov Function For Lienard-Type Nonlinear Systems

H. Miyagi, K. Yamashita

Proceedings Volume 0854, IECON '87: Motor Control and Power Electronics; (1987) https://doi.org/10.1117/12.942972
Event: IECON, Cambridge, 1987, Cambridge, MA, United States

Abstract

The direct method of Lyapunov is used to study the stability of a Lienard-type nonlinear system. The system is given in a form of n second-order ordinary differential equations. To establish the procedure for constructing Lyapunov function, a similar system is derived first, by multiplying both sides of the system equation by a transformation matrix. Then, a stability criterion for the Lienard-type nonlinear system, which introduces a new type Lyapunov function, is presented. The function obtained is a generalized Lyapunov function. The construction procedure given in this paper is applied to an example system represented by so-called Lienard's equation and the superiority of the proposed function is illustrated by numerical examples.

Citation Download Citation

H. Miyagi and K. Yamashita "A Generalized Lyapunov Function For Lienard-Type Nonlinear Systems", Proc. SPIE 0854, IECON '87: Motor Control and Power Electronics, (19 October 1987); https://doi.org/10.1117/12.942972

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