Solving polynomial static output feedback problems with PENBMI

Abstract

An algebraic formulation is proposed for the static output feedback (SOF) problem: the Hermite stability criterion is applied on the closed-loop characteristic polynomial, resulting in a non-convex bilinear matrix inequality (BMI) optimization problem for SIMO or MISO systems. As a result, the BMI problem is formulated directly in the controller parameters, without additional Lyapunov variables. The publicly available solver PENBMI 2.0 interfaced with YALMIP 3.0 is then applied to solve benchmark examples. Implementation and numerical aspects are widely discussed.