Comparison of several methods of H∞ filtering design for discrete-time linear systems

This paper is about robust H_∞ filtering design for linear system with polytopic uncertainties. The possible source of conservatism is explored by analyzing how the slack variables are introduced, such as the special structures etc. Then, based on the analysis, an iteration algorithm is proposed to reduce the conservatism. Since no special structures are required in the slack variables, it is shown that the algorithm can further reduce conservatism when the technique of introducing variables fails. In the end, three examples are presented to demonstrate the effectiveness of the algorithm and the relationship between introducing `outer´ and `inner´ variables is also illustrated.