Extension of V.M. Popov's Hyperstability Theory and its Application in Adaptive System Design

Abstract

The extension of V.K. Popov's hyperstability theory is presented in chis paper. It has been proved that a system is asymptotically stable by the definition of hyperstability if all the poles and zeros of the linear part of a system are in the left half complex plane. If in this case the transfer function of the system is not positive real, then a Eurwitz differential operator of proper degree can be introduced to reform the characteristic of nonlinear part of the system. A design of model reference adaptive control system is suggested by using the theorem obtained in this paper. Both “integration” and “proportion plus integration” parameter adaptation rules are used.