Robust control for uncertain hyperbolic partial differential equations

The problem of robust control for a class of hyperbolic partial differential equations under mixed uncertainties is addressed. A strong solution of the Cauchy 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. The derived control turns out to be a linear feedback controller containing as gain operator a solution of a corresponding operator Riccati equation. Robust control for one-dimensional wave equation is considered as an illustration of the suggested approach.