Control of rate constrained linear parameter varying systems

Linear parameter varying (LPV) systems are defined as linear systems whose dynamics depend on exogenous time-varying parameters. Typically, the parameter values are assumed to be confined to a prescribed set. Further assumptions may include restrictions on the parameter rates of variation. In this paper, the authors examine the stability and stabilization of LPV systems under various restrictions on the parameter variations. In particular, the authors employ computational methods to explicitly construct invariant and controlled invariant sets for LPV systems. These sets will allow one to either infer stability or construct stabilizing feedback. Such methods have been used extensively throughout the controls literature from a variety of contexts. The authors present methods for stability analysis and stabilization. These methods are applicable to a variety of constraints on parameter variations