Robust stabilization for discrete-time periodic systems with an ℋ∞-bounded uncertainty

In this paper the problem of robustly stabilizing a family of linear discrete-time periodic systems is studied. The family is characterized by H_∞ bounded perturbations to the numerator and denominator of the normalized coprime factorization of a nominal system. This problem gives an optimal stability margin √(1-||[M˜_i,N˜_i]||_H ²). The realization of the robust optimal periodic controller can be constructed by solving the periodic filtering Riccati equation and control Riccati equation. It is also shown that all optimal periodic controllers can be obtained via the Nehari´s extension approach