Approximate solutions to H2 optimization problems with H2 and H∞ constraints

In this paper a H₂ optimal control problem is considered in which the controllers are constrained to satisfy prescribed upper bounds on the H₂ and H_∞ norms of several closed-loop transfer functions. A sequence of H₂-cost/H₂-constraint problems is presented which aims at generating approximate solutions to the original problem - this may be viewed as a generalization of the so-called Law-son algorithm for Tchebyche approximation. Each such H₂/H₂ problem has a unique rational solution which can be computed through line search and spectral factorization. Under appropriate assumptions, it is shown that the sequence of optimal cost values for the H₂/H₂ problems is increasing and bounded from above (hence, it is convergent) and that, whenever the corresponding sequence of solutions converges, it does so to the solution of the original problem.