This paper deals with the robust stabilization of infinite dimensional systems subjected to stochastic and deterministic perturbations. First, we give conditions providing the stability of the parameterized system. Then, we investigate the maximization of the stability radius by state feedback. We establish conditions for the existence of suboptimal controllers. Using these conditions we characterize the supreme achievable stability radius via an infinite dimensional Riccati equation.

Robust Stabilization of Infinite Dimensional Systems Subjected to Stochastic and Deterministic Perturbations

Stability radii of infinite-dimensional systems subjected to unbounded stochastic perturbations

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.

Maximization of the Stability Radius of an Infinite Dimensional System Subjected to Stochastic Unbounded Structured Multi-perturbations With Unbounded Input Operator

In this paper we consider infinite dimensional systems which are subjected to stochastic structured multiperturbations. We first characterize the stability radii of these systems in terms of a Lyapunov equation and the corresponding Lyapunov inequalities. Then we investigate the problem of maximizing the stability radius by linear state feedback. We show that the supremal achievable stability radius can be determined via the resolution of a parametrized Riccati equation. Illustrative examples are included. Copyright © 2006 John Wiley & Sons, Ltd.

Stability radii of infinite dimensional systems with stochastic uncertainty and their optimization

We consider a class of linear infinite-dimensional systems subject to boundary uncertainties, which are linear and time-invariant. Using a deterministic approach to the design of stabilizing feedback controls, uniform exponential stability of the zero state is achieved. Lyapunov techniques are combined with Datko or Ichikawa theory. Three illustrative examples are presented.

S. E. Rebiai

Papers

Stability radii of infinite dimensional systems with stochastic uncertainty and their optimization

Stabilization of uncertain boundary control systems