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

Abstract

This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of n-th order linear time invariant (LTI) systems with n/sub u/ (resp. n/sub y/) independent inputs (resp. outputs). The algorithm is based on a "cone complementarity" formulation of the problem, and is guaranteed to produce a stabilizing controller of order m/spl les/n-max(n/sub u/,n/sub y/), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less or equal to that predicted by Kimura's (1994) generic stabilizability result (m/spl les/n-n/sub u/-n/sub y/+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis.