Minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems by one-sided boundary controls

Abstract

In this article we study the minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems when all the controls are acting on the same side of the boundary. We establish an explicit and easy-to-compute formula for this time with respect to all the coupling parameters of the system. The proof relies on the introduction of a canonical $UL$-decomposition and the compactness-uniqueness method.

Added reference [Wec82], comparison with it (in particular, Appendix B). Added counterexample if the assumption of [Rus78] is not satisfied (Appendix C). Added Figures. Corrected typos