AN EXACT SOLUTION TO GENERAL 4-BLOCK DISCRETE-TIME MIXED H-2 H-INFINITY PROBLEMS VIA CONVEX-OPTIMIZATION/

The mixed H-2/H-infinity control problem can be motivated as a nominal LQG optimal control problem subject to robust stability constraints, expressed in the form of an H-infinity norm bound. While at the presen t time there exist efficient methods to solve a modified problem consi sting on minimizing an upper bound of the H-2 cost subject to the H-in finity constraint, the original problem remains, to a large extent, st ill open. This paper contains a solution to a general four-block mixed H-2/H-infinity problem, based upon constructing a family of approxima ting problems. Each one of these problems consists of a finite-dimensi onal convex optimization and an unconstrained standard H-infinity prob lem. The set of solutions is such that in the limit the performance of the optimal controller is recovered, allowing one to establish the ex istence of an optimal solution. Although the optimal controller is not necessarily finite-dimensional, it is shown that a performance arbitr arily close to the optimal can be achieved with rational (and thus phy sically implementable) controllers. Moreover, the computation of a con troller yielding a performance epsilon-away from optimal requires the solution of a single optimization problem, a task that can be accompli shed in polynomial time.