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

• In this paper we establish the theory on the semiglobal classical solution to first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, and based on this, the corresponding exact boundary controllability and observability are obtained by a constructive method. Moreover, with the linearized Saint-Venant system and the 1-D linear wave equation as examples, we show that the number of both boundary controls and boundary observations can not be reduced, and consequently, we conclude that the exact boundary controllability for a hyperbolic system in a network with loop can not be realized generically.
Mathematics Subject Classification: Primary: 93B05, 93B07; Secondary: 35L50.

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