In this paper we consider infinite dimensional systems subjected to stochastic structured multiperturbations. We address the problem of robustness optimization with respect to state feedback but allow both unbounded input and perturbations. Conditions are derived for the existence of a stabilizing controller ensuring that the norm of the closed loop operator below a prespecified bound. Such controllers will be called suboptimal controllers. The suboptimality conditions are obtained in terms of a Riccati equation which satisfies an operator inequality. Finally, we give a lower bound for the supremal achievable stability radius via the Riccati equation.

The issue of robustness of stability has been prominent in the literature on control theory over the last two decades. An important state-space approach to robustness analysis is the stability radii theory. The robust stability problems of infinite dimensional systems subjected to stochastic bounded structured perturbations have been studied using the stability radius approach. In the applications it is important to study these problems in the case where the perturbations operator structure are unbounded, because it covers the case of partial differential equations with boundary and ..

The issue of robustness of stability has been prominent in the literature on control theory over the last two decades. An important state-space approach to robustness analysis is the stability radii theory. The robust stability problems of infinite dimensional systems subjected to stochastic bounded structured perturbations have been studied using the stability radius approach. In the applications it is important to study these problems in the case where the perturbations operator structure are unbounded, because it covers the case of partial differential equations with boundary and ...