Robust Controller Synthesis Under Markovian Mode Switching With Periodic LTV Dynamics

In this letter, we propose novel LMI-based controller synthesis frameworks for discrete-time Markov-jump systems with periodically time-varying dynamics. We discuss necessary and sufficient conditions for mean square stability and derive Lyapunov-like conditions for stability assurance. To relax strict stability requirements, we introduce a new criterion that does not require the Lyapunov function to decrease at each time step. Further, we incorporate these stability theorems in LMI-based controller synthesis frameworks while considering two separate problems: minimizing an upper bound of a quadratic cost and maximizing the region of attraction, all while guaranteeing stability. Numerical simulations verify the controllers’ stability and showcase its applicability to fault-tolerant control.