Static output feedback stabilization with prescribed degree of stability

Abstract

The problem of finding a static output feedback matrix is restated. The new formulation replaces the solution of a set of inversely coupled Lyapunov inequalities with the simultaneous solution to an algebraic Riccati inequality and a Lyapunov inequality. An algorithm is developed based on the restated problem. Unlike previous algorithms, the algorithm is noniterative in linear matrix inequality (LMI) solutions. The algorithm may be used to prescribe a given degree of stability, while keeping the static output feedback gain small. Use of the algorithm is demonstrated via an example.