Interactive loop-shaping design of MIMO controllers

It is shown that many classical and singular value loop shaping problems are closed-loop convex. Consequently, loop shaping problems can be solved by efficient numerical methods. In particular, it can be determined whether or not a compensator exists that satisfies a given set of loop shaping specifications. Loop shaping design problems that are formulated as classical optimization problems, e.g., maximizing bandwidth subject to given margin and cutoff specifications, can be solved by direct numerical methods for quasiconvex optimization. A consequence of these observations is that closed-loop convex design methods can be used to do compensator design in a classical loop shaping framework which is familiar to many control engineers