Robust Regulator for Markov Jump Linear Systems with Random State Delays and Uncertain Transition Probabilities

The recursive robust regulation problem for Markov jump linear systems with state delay is investigated. The random delay belongs to a known interval and its maximum variation rate is considered. The transition probabilities matrix is subject to polytopic uncertainties. We model the delay by a Markov chain and obtain a delay-free Markovian system, through the augmented system approach. Based on combination of regularized least-squares with polytopic uncertainties and penalty function method, we propose a mode-dependent state-feedback control. The solution is given in terms of coupled Riccati equations presented in a symmetric matrix arrangement. With a numerical example, we compare our approach with other robust controllers from the literature.