Controllability and Stabilizability Theory for Linear Partial Differential Equations: Recent Progress and Open Questions

This paper is an assessment of the current state of controllability and observability theories for linear partial differential equations, summarizing existing results and indicating open problems in the area. The emphasis is placed on hyperbolic and parabolic systems. Related subjects such as spectral determination, control of nonlinear equations, linear quadratic cost criteria and time optimal control are also discussed.