Trajectory-dependent filter design for discrete-time switched linear systems

This paper is devoted to trajectory-dependent filtering design for discrete-time switched linear systems. Based on a nonconvex Lyapunov function of min type, stability conditions and quantities similar to H2H2 and H∞H∞ norms are calculated. It is shown that the optimal filter design reduces to the solution of a convex optimization problem expressed in terms of linear matrix inequalities (LMIs). It is also shown that the global optimal filter presents an observer-based structure that is more suitable for implementation purposes due to its simplicity. Two illustrative examples are included for comparison.