An interpolation approach to multiobjective H-infinity design

A problem of practical importance is to find a linear controller that shapes the closed loop frequency responses in some desirable fashion. When the magnitude of the target shapes is specified, this problem may be cast as that of finding a controller such that several H-infinity, norms satisfy specified bounds. In this paper we show that, under suitable assumptions, an exact solution to this multiobjective H-infinity problem can be obtained. The method we propose requires the solution to. (1) a finite-dimensional linear matrix inequality problem, and (2) a standard single objective H-infinity problem for a suitably constructed auxiliary plant. We illustrate the results with a numerical example.