Multiobjective H/sub 2//H/sub /spl infin//-optimal control via finite dimensional Q-parametrization and linear matrix inequalities

The problem of multiobjective H/sub 2//H/sub /spl infin// optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer (1995). The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H/sub 2/ and H/sub /spl infin// norms. Suboptimal solutions are computed using finite dimensional Q-parametrization. The objective value of the suboptimal Qs converges to the true optimum as the dimension of and is increased. State space representations are presented which are the analog of those given by Khargonekar and Rotea (1991) for the H/sub 2/ case. A simple example computed using finite impulse response Qs is presented.