Recursive Robust Regulator for Discrete-Time Markovian Jump Linear Systems

In this paper, we propose a robust regulator for discrete-time Markovian jump linear systems (DMJLS) subject to structured parameter uncertainties. States of Markov chain are considered known at each instant and the transition probabilities matrix is time-varying. The framework proposed to deal with this problem is developed through a regularization approach based on robust least-squares and penalty functions. Recursive solutions in terms of coupled Riccati equations, which do not depend on any auxiliary parameter to be tuned, are provided. These equations resemble the recursive solutions of DMJLS standard regulators when the system is not subject to uncertainties. Conditions for convergence and stability of this robust regulator are established. Numerical examples present comparative studies considering the proposed robust regulator, the standard linear quadratic regulator, and an H∞-controller for DMJLS.