A Novel Approach to H2 and H8, Filter Design for Discrete-time Switched Affine Systems

This paper focuses on solving H-2 and H-infinity filtering problems for discrete-time switched affine systems. By constructing a discrete-time affine filtering error system, an observer-based filter and its corresponding switching function can be obtained by solving the linear matrix inequalities. For discrete-time switched affine systems, the performance indexes of the system in this neighborhood cannot be analyzed due to the existence of affine terms. The technique proposed in this note leads the system's trajectory to the limit cycle so that the resulting conditions can consider the weighted H-2 and H-8 performance level of the system. In addition, it is proved that the H-2 and H-8 guaranteed cost is upper bounded and the upper boundaries are formulated by solving an optimization problem. Finally, two numerical examples are given to verify the theory.