Recursive Robust Control for Uncertain Discrete-Time Markovian Jump Linear Systems with Markov Time-Delays

We deal with the recursive robust control problem for uncertain discrete-time Markovian jump linear systems with Markov time-delay. We assume all matrices of the system are subject to norm-bounded parametric uncertainties. By application of the lifting method and modeling of time-varying delay as a mode-dependent Markov chain, the delay system is converted to an augmented delay-free Markovian jump linear system. The delay-independent state-feedback control is then deduced by the robust regularized least-squares approach. The proposed solution is given in terms of augmented coupled Riccati equations presented through a symmetric matrix arrangement. With a numerical example, we evaluate the proposed control and compare its performance with a control approach.