Filtering of two-dimensional periodic Roesser systems subject to dissipativity

In this note, the problem of dissipativity-based filtering of two-dimensional (2D) periodic Roesser systems is investigated. A discrete-time periodic Roesser model extensively used in practical systems is introduced to describe 2D periodic systems. Moreover, it is assumed that the periods of the augmented system in horizontal and vertical directions are the same, which can greatly simplify stability analyses. By resorting to the periodic Lyapunov functional approach that depends on periodical property of the augmented system, less conservative results for the existence of 2D periodic filter are presented to ensure the asymptotic stability and 2D (Q1,Q2,Q3)−β-dissipativity. Particularly, the parameters of 2D periodic filter are derived with convex optimization method. Simulation results are provided to verify the effectiveness and merits of the theoretical findings. In addition, the correlation between optimal dissipative performance indices and different Lyapunov functions is revealed.