Mixed H2/H∞ - control with an output-feedback compensator using parameter optimization

In this paper we present a different approach to the mixed H₂/H_∞-control problem. The procedure involves the formulation of a finite-time cost functional that represents an H_∞-bound in a H₂-optimization setting through a specific parametrization of the worst-case disturbance. One benefit of this formulation is that the ensuing optimization procedure does not require an initial controller guess to be stabilizing. Our approach also represents a non-Riccati based method for the mixed H₂/H_∞-control problem, it allows the incorporation of linear controllers with arbitrary structure and order; a problem that has not yet been solved in a numerically efficient manner. Here, we define a time-domain cost functional that, as t_∫ → ∞, will lead to the solution of an optimal H₂-norm control problem with an H_∞-norm bound constraint (i.e T_{z∞ w∞∞} ≪ γ where γ is a prespecified parameter). Parameterizations of the controller and the worst-case disturbance will lead naturally to the use of numerical parameter optimization techniques. Finally an example will illustrate the tradeoff between the H₂- and the H_∞-design objective.