Multiobjective H 2 =h 1 -optimal Control via Finite Dimensional Q-parametrization and Linear Matrix Inequalities

The problem of multiobjective H2=H1 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 14]. The problem is formulated as a convex semidef-inite program (SDP) using the LMI formulation of the H2 and H1 norms. Suboptimal solutions are computed using-nite dimensional Q-parametrization. The objective value of the suboptimal Q's converges to the true optimum as the dimension of Q is increased. State space representations are presented which are the analog of those given by Khargonekar and Rotea 11] for the H2 case. A simple example computed using FIR (Finite Impulse Response) Q's is presented.