An exact solution to general 4-blocks discrete-time mixed H2/H∞ problems via convex optimization

The mixed H₂/H_∞ control problem can be motivated as a nominal LQG optimal control problem, subject to robust stability constraints, expressed in the form of an H_∞ norm bound. A related modified problem consisting of minimising an upper bound of the H₂ cost subject to H_∞ 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_∞ problem.