The /spl rho/ performance measure: a new tool for controller design with multiple frequency domain specifications

Multiobjective frequency domain design aims to find a controller that gives desirable properties to several closed loop frequency responses simultaneously. This problem may be cast as a problem of finding a controller such that the worst-case /spl Hscr//sub /spl infin// norm, i.e. the largest among several /spl Hscr//sub /spl infin// norms, satisfies a prespecified bound. The authors define an upper bound, the /spl rho/ measure, for the worst-case /spl Hscr//sub /spl infin//, norm in terms of a scaled /spl Hscr//sub /spl infin// cost function. The authors show that the problem of finding a controller that minimizes /spl rho/ can be reduced to a finite dimensional convex program for the unknown scales and a standard /spl Hscr//sub /spl infin// problem. The authors give affine matrix inequalities for controller synthesis when the scales are restricted to constant matrices. A numerical example is used to illustrate the advantages of the authors' formulation, over the single objective /spl Hscr//sub /spl infin//, formulation, for solving multiobjective /spl Hscr//sub /spl infin// problems.