Well-posedness of boundary control systems

Abstract

Boundary control systems are an important class of infinite dimensional control systems. A key question is whether the mappings from input state, input/output, state/input and initial state/final state are well-defined bounded linear maps. When all four mappings are well-defined and bounded, the problem is said to be well-posed. This thesis examines boundedness of the input/output map.

Continuity of the input/output map for a boundary control system is shown through the system transfer function. Our approach transforms the question of boundedness of the input/output map of a boundary control system into boundedness of the solution to a related elliptic problem. Boundedness is shown for a class of boundary control systems with Dirichlet, Neumann or Robin boundary control. Use of the transfer function in approximations is also demonstrated.