A Reduced-Complexity Polytopic Control Approach for Uncertain quasi-LPV Descriptor Systems

Abstract

This paper presents an extension of our previously established polytopic approach to obtain an equivalent reduced complexity polytopic representation of uncertain quasi-linear parameter varying (quasi-LPV) descriptor systems. The proposed approach yields a polytopic representation with 2(r + ℓ) vertices for r scheduling variables and ℓ uncertainty terms instead of the conventional 2r polytopic form. The resulting polytopic form is strictly equivalent to the uncertain quasi-LPV model within a compact set. The decreased number of vertices allows for fewer linear matrix inequalities (LMI) design conditions and thus a decreased numerical complexity. Additionally the proposed approach allows for a new solution for dealing with parametric uncertainties reducing the conservatism with respect to the feasibility of LMI design conditions. Both numerically and physically motivated examples are given to demonstrate the interests of the new control approach with respect to existing uncertain polytopic approaches.