A novel two-stage strategy for robust H∞ filter design of uncertain discrete-time systems

This paper studies the robust H∞ filter design problem for discrete-time linear system with polytopic uncertainty. Differing from existing ideas in the literature to reduce filtering conservatism, the present article proposes a less conservative two-stage algorithm to handle this issue by stepwisely recovering and utilizing matrix variable information of analysis condition. This algorithm is formulated by virtue of the combined matrix inequality with a prefixed binary choice signal, which is composed of direct design condition with nonlinear matrix variable inequality and its corresponding linearized one. In general, a more relaxed matrix variable structure is derived based on improved scalar parameter approach from the perspective of eigenvalue theory, which is then applied to obtain less conservative filter design condition with linearized matrix variable inequality in the first stage of provided algorithm. With some solved variables in stage one, that nonlinear matrix variable inequality based design condition is transformed into linear version, and in the second stage it will be used to further optimize the filtering performance level via picking up the lost matrix variable information of stage one. Finally, the advantages of the given algorithm are clearly illustrated by two examples.