Robust Filtering for Linear Polytopic Discrete-Time Periodic Systems*

This paper is concerned with the problems of robust H∞ and guaranteed variance filtering for linear discrete-time periodic systems with polytopic-type parameter uncertainty in the matrices of the system state-space model. Filtering methods are derived for designing linear periodic asymptotically stable filters with either a prescribed upper-bound on the l2-gain from the noise signals to the estimation error, in the H∞ case, or a guaranteed upper-bound on the average steady-state variance of the estimation error variance, for the guaranteed variance filtering, in spite of the parameter uncertainty. The proposed methods are based on parameter-dependent Lyapunov functions and are given in terms of linear matrix inequalities. The potentials of the proposed filtering methods are demonstrated by an example.