Robust controller design via linear programming

This paper presents a linear programming (LP) algorithm for an optimal robust controller design under parametric uncertainty. This algorithm is based on the convex robust controller parametrization which is available for uncertain plants in the form G_δ: {(y/z)=G(s)(u/w)/w=δ^T_z, where G(s) is the nominal plant, w is a scalar input and δ is the uncertain vector in R^m. The algorithm proposed is a sequence of the standard linear programming problems of growing dimension which approximate the initial problem. A dual interpretation to the problem is derived. It is shown that the dual problem can be solved with an LP algorithm similar to the primal one. Two examples show that a combination of the primal and dual algorithms is an effective way to solve a problem of the uncertainty radius maximization under stability constraint