A cone complementarity linearization algorithm for static output-feedback and related problems

This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with n_u (respectively, n_y) independent inputs (respectively, outputs). The algorithm is based on a “cone complementarity” formulation of the problem and is guaranteed to produce a stabilizing controller of order m⩽n-max(n_u,n_y), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura´s generic stabilizability result (m⩽n-n_u-n_y+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis