Switching among structured stabilizing controllers

In this paper we consider the problem of designing a controller K that consists of a set of structured stabilizing components {K^m}_m ⁿ = 1. At each time instant depending on the mode J_m of operation, the corresponding component K^m is used. We seek conditions so that a controller, implemented in this form, minimizes the worst case l_infin-induced norm under arbitrary switching of the controller among n components, while providing a pre-specified performance level gamma_m in each operational mode J_m. Based on the Youla-Kucera parameterization, the design problem can be converted into a sequence of linear programming problems, the solutions of which provide an approximate solution of the original problem with any given precision. A numerical example is included to demonstrate the efficiency of algorithms.