On the convergence of optimal, mixed-specification control problems

Considers a constrained optimal control problem, in which the ℋ_∞ norm of some transfer matrix is to remain bounded by some number while an objective function is minimized. All ℋ₂/ℋ∞, l¹/ℋ_∞ and time domain constrained ℋ_∞ are contained in the author´s formulation. It is shown that a suboptimal solution may be computed by solving a finite dimensional, convex optimization problem. This problem may be constructed a priori in terms of the data and is usually large. Hence an iterative algorithm with guaranteed convergence is also given for the computation of an approximate solution