A Novel RPI Set Computation Method for Discrete-time LPV Systems with Bounded Uncertainties

Set invariance plays a fundamental role in the analysis and design of linear systems. This paper proposes a novel method for constructing robust positively invariant (RPI) sets for discrete-time linear parameter varying (LPV) systems. Starting from the stability assumption in the absence of disturbances, we aim to construct the RPI sets for parametric uncertain system. The existence condition of a common quadratic Lyapunov function for all vertices of the polytopic system is relaxed in the present study. Thus the proposed method enlarges the application field of RPI sets to LPV systems. A family of approximations of minimal robust positively invariant(mRPI) sets are obtained by using a shrinking procedure. Finally, the effect of scheduling variables on the size of the mRPI set is analyzed to obtain more accurate set characterization of the uncertain LPV system. A numerical example is used to illustrate the effectiveness of the proposed method.

I. Introduction

Many control and fault diagnosis problems can be naturally formulated, analyzed, and solved in a set-theoretic framework [1]. Sets are naturally involved in control and fault diagnosis fields by considering system uncertainties and physical constraints. Especially, invariant sets play an important role in the solutions of many control and fault diagnosis problems in complex systems [2] [3].