Abstract:In this work, the problem of stabilization of general systems of linear transport equations with indomain and boundary couplings is investigated. It is proved that the unstable part of the spectrum is of finite cardinal. Then, using the pole placement theorem, a linear full state feedback controller is synthesized to stabilize the unstable finite-dimensional part of the system. Finally, by a careful study of semigroups, we prove the exponential stability of the closed-loop system. As a by product, the linear c… Show more
“…C 1 norm) but that is still exponentially stable? For the linearized system this is very likely to be true, using spectral tools as shown in [12, Section 5.6] (see also [80,72])…”
“…C 1 norm) but that is still exponentially stable? For the linearized system this is very likely to be true, using spectral tools as shown in [12, Section 5.6] (see also [80,72])…”
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.