Feedback Stabilization of Linear Systems with Parametric Uncertainties: a Multimodel Guaranteed Cost Approach

Abstract

This paper proposes the framework of multimodel guaranteed cost (MMGC) control for the robust feedback stabilization of LTI plants subject to parametric uncertainties. The idea of this method is as follows. First we partition the domain of uncertain parameters into subregions whose sizes are determined by a chosen "resolution level." Then, on each subregion we define an Algebraic Riccati Equation (ARE), such that the existence of a positive definite solution guarantees robust stability over the subregion. Finally, we search for a common feedback law which results in a positive definite solution for each of these ARE. This search is performed by solving an auxiliary minimization problem (AMP), which is made convex by choice of a parameter.