Model Reduction of Strongly Stable Nonstationary LPV Systems

Abstract

This paper deals with the model reduction of nonstationary linear parametervarying (NLPV) systems. Our interest in LPV models is motivated by the desire to control nonlinear systems along prespecified trajectories. LPV models arise naturally in such scenarios as a method to capture the possible nonlinear dynamics, while maintaining a model that is amenable to control synthesis. Frequently, when pursuing such an LPV formulation, one ends up with models of relatively large dimension. Accordingly, finding control syntheses for such models, which usually involves solving a number of linear operator inequalities as discussed in [5], requires substantial computation. For this reason, developing a theory that provides systematic methods of approximating such models is beneficial.