Stability of Linear Discrete-Time Periodic Systems with Time-Delay*

This paper deals with the problem of asymptotic stability of linear discrete-time periodic systems with a delayed state. A stability criterion independent of the time-delay length as well as a delay-dependent criterion are proposed, where the former applies to the case of a constant time-delay and the latter allows for a time-varying delay lying in a given interval. The developed stability criteria builds on Lyapunov-Krasovskii functionals and are given in terms of linear matrix inequalities. Extensions of the stability results for periodic systems with polytopic-type parameter uncertainty in the state-space matrices are also derived using parameter-dependent Lyapunov-Krasovskii functionals.