Robust filtering design of piecewise discrete time linear systems

This work presents two filter design methods for piecewise discrete time linear systems based on a piecewise Lyapunov function. It is shown that the resulting filtering error system is globally stable with guaranteed H_∞ or generalized H₂ performance, and the filter gains can be obtained by solving a set of linear matrix inequalities that is numerically feasible with commercially available software. Two simulation examples are also given to illustrate the performance of the proposed approaches.