AN EXACT SOLUTION TO GENERAL SISO MIXED H-2 H-INFINITY PROBLEMS VIA CONVEX-OPTIMIZATION/

The mixed H-2/H-infinity, control problem can be motivated as a nomina l LQG optimal control problem, subject to robust stability constraints , expressed in the form of an H-infinity, norm bound. A related modifi ed problem consisting on minimizing an upper bound of the H-2 cost sub ject to H-infinity, constraints was introduced in [1]. Although there presently exist efficient methods to solve this modified problem, the original problem remains, to a large extent, still open. In this paper we propose a method for solving general discrete-time SISO H-2/H-infi nity problems. This method involves solving a sequence of problems, ea ch one consisting of a finite-dimensional convex optimization and an u nconstrained Nehari approximation problem.