Multi-Model Adaptive Regulation for a Family of Systems Containing Different Zero Structures

Abstract

An adaptive regulator is proposed for parameter dependent families of linear systems subject to changes in the zero structure. Adaptation is required for the parameter dependent family of plants but continuous adaptive regulation is limited by relative degree and right half plane zeros. A form of adaptive regulation is presented that accommodates parameter induced changes in the zero structure. The conditions for regulation divide the parameter space into disjoint sets thereby defining subfamilies of plants. These plant subfamilies guide controller design. Controller stability is guaranteed by Linear Matrix Inequalities (LMI) and a switch logic based on Lyapunov functions.