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In this paper we establish the theory on semiglobal classical solution tofirst order quasilinear hyperbolic systems with a kind of nonlocal boundaryconditions, and based on this, the corresponding exact boundary controllabilityand observability are obtained by a constructive method. Moreover, with thelinearized Saint-Venant system and the 1-D linear wave equation as examples, weshow that the number of both boundary controls and boundary observations cannot be reduced, and consequently, we conclude that the exact boundarycontrollability for a hyperbolic system in a network with loop can not berealized generically.

Exact boundary controllability and observability for first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions