H2-optimal control with an H[infinity]-constraint The state feedback case

Abstract

In this paper we consider a mixed H2/H[infinity]-optimal control problem. It is assumed that the plant as well as the feedback controller are finite-dimensional and linear time-invariant, and that the plant state is available for feedback. More specifically, among all the state-feedback controllers that minimize the H2-norm of a closed loop transfer matrix, we give necessary and sufficient conditions for the existence of a controller that also satisfies a prescribed H[infinity]-norm bound on some other closed loop transfer matrix. When these conditions are met, the solution to the above problem is also a global solution to the contrained optimization problem of minimizing an H2-norm performance measure subject to an H[infinity]-norm constraint. We also give state-space formulae for computing the solutions. Some easily checkable sufficient conditions for the existence of solutions are given. Finally we give an example in which all solutions to the constrained optimization problem are necessarily dynamic, i.e. there is no static gain solution even though plant state is available for feedback.