Boundary control design for conservation laws in the presence of measurement disturbances

Boundary feedback control design for systems of linear hyperbolic conservation laws in the presence of boundary measurements affected by disturbances is studied. The design of the controller is performed to achieve input-to-state stability (ISS) with respect to measurement disturbances with a minimal gain. The closed-loop system is analyzed as an abstract dynamical system with inputs. Sufficient conditions in the form of dissipation functional inequalities are given to establish an ISS bound for the closed-loop system. The control design problem is turned into an optimization problem over matrix inequality constraints. Semidefinite programming techniques are adopted to devise systematic control design algorithms reducing the effect of measurement disturbances. The effectiveness of the approach is extensively shown in several numerical examples.