Stability of Feedback Systems with Product-Type Nonlinearities.

Abstract

For the study of the stability of nonlinear feedback systems, it is common to use a Lure-type Lyapunov function, and the most general approach by which to construct the Lyapunov function is the method based on the Popov criterion. In the case of product-type nonlinear feedback, however, the Lure-type Lyapunov function is not adapted well. Thus, the quadratic form of statevariables has been employed as a Lyapunov function. The Lyapunov method gives, generally, only the sufficient conditions for obtaining stability. Hence, it is important for system engineers to determine the Lyapunov function which guarantees a wider stability region. This paper presents Lyapunov functions for the stability analysis of dynamical systems with product-type nonlinear feedbacks. Stability criteria which introduce extended Lyapunov functions are given. The superiority of the function proposed is indicated by numerical examples.