A method of constructing non-Lure type Lyapunov function for nonlinear control systems.

概要

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In this paper, the direct method of Lyapunov is used to analyze a nonlinear control system. A non-Luré type Lyapunov function which gives wider stability region than the conventional Luré type Lyapunov function is presented. This function includes a new extra term having not appeared in the Luré type function. In fact, the Luré type function has been confined to the "quadratic-plus-integrals of the nonlinearities" type, and thus, in many cases, has given too conservative results for the stability. The construction procedure developed in this paper, for the new type Lyapunov function, is systematic and is essentially based on the generalized Popov criterion established by Moore and Anderson.This new technique is applied to the singlemachine system with a control equipment modeled by a linear 1st-order response and the stability of the system is studied. In this 3rd-order system, it is shown that the proposed non-Luré type Lyapunov function gives considerable improvement of stability boundary estimates over that given by the Luré type Lyapunov function.
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