ETA-INFINITY-CONTROL WITH TIME-DOMAIN CONSTRAINTS - THE INFINITE-HORIZON CASE

It has been shown recently that time domain constraints can be incorporated into H(infinity)-optimal control problems when the constraints are enforced over a finite horizon, i.e. over a finite number of sample instants. This is done in (Sideris and Rotstein, 1993; Rotstein and Sideris, to appear) where the finite horizon problem is reduced into a finite dimensional, convex, but generically nondifferentiable optimization program. In this paper, the infinite horizon case is addressed. It is shown that when the horizon length goes to infinity, the solutions to the finite horizon problems converge to a solution of the infinite horizon problem. Moreover, a simple modification of the finite horizon problems guarantees convergence to a solution that is easily approximated by a finite dimensional transfer function.