Repetitive Control of Discrete-Time Markov Jump Linear Systems

In this paper a mode-dependent repetitive controller design for discrete-time Markov Jump Linear Systems (MJLS) is proposed for tracking a periodic reference signal. By employing ideas from the lifting technique, the discrete-time MJLS and the repetitive controller structure are transformed into a stochastic two-dimensional model that differentiates the control and learning actions involved in the repetitive controller structure. For this transformed model, sufficient conditions are derived for the closed-loop control system to be mean square asymptotically stable by utilizing tools from stochastic systems theory and Lyapunov techniques. Results from numerical simulations on a stochastic switching tunnel diode circuit are presented to corroborate the proposed method.