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 that 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. A heating boundary control process is given as an illustration of the suggested approach.
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