Optimal Periodic Filtering of Discrete-Time LTI Systems

This paper is entirely devoted to the study of optimal linear periodic filters for discrete-time LTI systems. A new performance index inspired by the well-known H-2 norm of LTI systems, is proposed to take into account time-varying disturbance characteristics in both deterministic and stochastic frameworks. For that class of design problems, the optimality conditions show that the periodic filter in the observer-form outperforms the classical LTI filter. They are expressed through LMIs being solved by the machinery available in the literature. For completeness, the design problem is reformulated and solved in the realm of periodic filtering. Academic examples, simulated with the Monte Carlo method, illustrate the theoretical results.