Rank-one LMI approach to simultaneous stabilization of linear systems

Following a polynomial approach to control design, the simultaneous stabili zation by a controller of given fixed order of a family of SISO linear syst ems is interpreted as an NP-hard BMI feasibility problem. Upon formulating this BMI problem as an LMI problem with an additional non-convex rank const raint, two simultaneous stabilization methods are then proposed, The first method is a heuristic algorithm performing rank minimization by potential r eduction. The second method hinges upon necessary conditions and sufficient conditions for simultaneous stabilization derived from geometric propertie s of the intersection of a set of ellipsoids. Both methods are then illustr ated by numerical examples. (C) 1999 Elsevier Science B.V. All rights reser ved.