Stabilization for discrete-time LPV systems with Markovian switching under partially known transition probabilities

Abstract

This paper investigates the stabilization problem for a class of discrete-time linear parameter-varying (LPV) systems with Markovian switching by using a parameter-dependent Lyapunov function method. A key point of this work relaxes discrete-time Markovian jump systems whose subsystems are described by discrete-time linear time-invariant (LTI) dynamics to discrete-time LPV systems with Markovian switching whose subsystems are described by discrete-time LPV dynamics. Meanwhile, the special assumption of completely known transition probability is relaxed to more general case that transition probability are partly known. Moreover, the proposed control technique for the discrete-time LPV systems with Markovian switching is used to solve the stabilization problem of turbofan-engine. Firstly, a state-feedback controller is designed, and the design problem can be reduced to a set of linear matrix inequalities (LMIs) feasibility problem. Then, a turbofan-engine example is given to demonstrate the applicability of the main results.