H∞ output control of discrete-time systems via convex optimization

This paper presents a convex optimization approach to (nearly) optimal H∞ output control problem of discrete-time systems. By using nonlinear matrix valued mapping.it is shown that the H output problem can be formulated as minimization of a linear objective function over a convex set inn (n+1)+1 dimensional space where n is the system dimension. Under the detectability and stabilizability conditions,the set is bounded. The H norm of the closed- loop system yielded by this method can come arbitrarily close to the minimum H norm. The method proposed can handle the additional convex constraints.