An exact solution to general 4-blocks discrete-time mixed H/sub 2//H/sub /spl infin// problems via convex optimization

The mixed H/sub 2//H/sub /spl infin// control problem can be motivated as a nominal LQG optimal control problem, subject to robust stability constraints, expressed in the form of an H/sub /spl infin// norm bound. A related modified problem consisting of minimising an upper bound of the H/sub 2/ cost subject to H/sub /spl infin// constraints was introduced in Bernstein and Haddad (1989). Although there presently exist efficient methods to solve this modified problem, the original problem remains, to a large extent, still open. Sznaier (1993) developed a method to solve exactly the simpler SISO case. In this paper the authors extend this method to general MIMO systems. As in Sznaiers' paper, the main result of this paper shows that the proposed method involves solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and an unconstrained H/sub /spl infin// problem.