Solution of the stochastic $\mathcal{H}_{\infty}$-optimization problem for discrete time linear systems under parametric uncertainty

The stochastic $\mathcal{H}_{\infty}$-optimization problem for a linear discrete time system with uncertain parameters is formulated and solved. The system operates in the presence of Gaussian random disturbances. The original problem with parametric uncertainty is reduced to the stochastic $\mathcal{H}_{\infty}$-optimization problem without uncertainty and having one extra input, which is essentially the mixed $\mathcal{H}_2/ \mathcal{H}_{\infty}$-optimization problem. In a sense, the problem considered in this paper incorporates the classical $\mathcal{H}_2/ \mathcal{H}_{\infty}$- and $\mathcal{H}_{\infty}$-optimization problems as limiting cases.