Robustness approach to envelope-constrained filtering

This paper is concerned with the maximum robustness design of envelope-constrained filters with uncertain input (ECUI). It is shown that the maximum robustness ECUI filter design can be formulated as a minimax optimization problem in which the set of feasible filters is characterized by nonsmooth matrix inequalities. On the basis of the use of a newly developed transformation technique and the use of standard linear programming and quadratic programming, an efficient design algorithm is developed to solve this problem. The attractive feature of the proposed algorithm is that the ECUI filter thus designed can allow for the greatest uncertainty in the input signal while still achieving the acceptable filter performance. A numerical example is given to illustrate the effectiveness of the algorithm.