An interpolation approach to multiobjective H∞ 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 are specified, this problem may be cast as that of finding a controller such that several H _∞ norms satisfy prespecified bounds. In this paper we show that under suitable assumptions on the plant under control, an exact solution to this multiobjective problem H_∞ problem can be obtained. The method we propose requires the solution to: (1) a finite dimensional convex program, and (2) a standard single objective H_∞ problem for a suitably constructed auxiliary plant. We illustrate the results using a numerical example. The example shows that the conventional approach of lumping the individual objectives into a single H_∞ objective may be unduly conservative when compared with an exact solution to the multiobjective H_∞ problem