Robust stability and control of uncertain linear discrete-time periodic systems with time-delay

This paper deals with the problems of robust stability analysis and robust control of linear discrete-time periodic systems with a delayed state and subject to polytopic-type parameter uncertainty in the state-space matrices. A robust stability criterion independent of the time-delay length as well as a delay-dependent criterion is 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 robust stability criteria are based on affinely uncertainty-dependent Lyapunov–Krasovskii functionals and are given in terms of linear matrix inequalities. These stability conditions are then applied to solve the problems of robust stabilization and robust H∞H∞  control via static periodic state feedback. Numerical examples illustrate the potentials of the proposed robust stability and control methods.