Filtering for uncertain periodic piecewise systems with dissipativity specifications

This paper investigates the dissipative filtering problem of discrete-time uncertain periodic piecewise systems. Firstly, the sufficient conditions that can ensure the exponential stability and (Q, S, R) dissipative performance of periodic piecewise systems are derived by constructing the Lyapunov function with periodic parameters. To design the optimal parameters of the filter, we resort to an effective technique - the slack matrix - for transforming these results into the semi-definite programing problem (SDP) that is tractable in the YALMIP toolbox. Finally, numerical examples are given to verify the effectiveness of the obtained results.