Static output feedback stabilization of linear and nonlinear systems

The static output feedback stabilization problem for linear and nonlinear (affine) systems is discussed. A novel necessary and sufficient condition for linear systems is proposed. For nonlinear systems a sufficient condition is established and a (partial) converse is also discussed. The nonlinear formulation is used to derive a simple characterization of stabilizing static output feedback control laws for linear systems in terms of the intersection of two convex sets and a (generally) nonconvex set. This characterization is used to establish a series of simple obstructions to the solvability of the problem for linear SISO systems. A fully worked out example complete the paper.