The problem of robust boundary control for a class of infinite dimensional systems under mixed uncertainties is addressed. A strong solution of the Dirichlet boundary problem corresponding to the perturbed evolution operator is introduced. The Lyapunov function approach is used for proving that there is a controller which stabilizes this class of systems under the presence of smooth enough internal and external perturbations and guarantees some tolerance level for the joint cost functional. The derived control consists of two parts: a compensating one and a linear feedback controller with a gain operator which is a positive inverse solution of a corresponding operator Riccati equation. A heating boundary control process is given as an illustration of the suggested approach.
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