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

It has been shown recently that time domain constraints can be incorpo rated into H(infinity)-optimal control problems when the constraints a re enforced over a finite horizon, i.e. over a finite number of sample instants. This is done in (Sideris and Rotstein, 1993; Rotstein and S ideris, to appear) where the finite horizon problem is reduced into a finite dimensional, convex, but generically nondifferentiable optimiza tion program. In this paper, the infinite horizon case is addressed. I t is shown that when the horizon length goes to infinity, the solution s to the finite horizon problems converge to a solution of the infinit e horizon problem. Moreover, a simple modification of the finite horiz on problems guarantees convergence to a solution that is easily approx imated by a finite dimensional transfer function.