Abstract. In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is regular and derive various properties of its transfer functions, which are potentially useful for controller design. Our results remain valid for a wide class of processes governed by symmetric hyperbolic systems.Mathematics Subject Classification. 93D09, 93D25, 80A20, 35L50.

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International audienceThe paper is concerned with the control of a fluid flow system gov-erned by nonlinear hyperbolic partial differential equations. The control and the output observation are located on the boundary. We study local stability of spatially heterogeneous equilibrium states by using Lyapunov approach. We prove that the linearized system is exponentially stable around each subcritical equilibrium state. A systematic design of proportional and integral controllers is proposed for the system based on the linearized model. Robust stabilization of the closed-loop system is proved by using a spectrum method

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Abstract.The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stability of closed-loop system achieved by some stabilizing output feedback laws may be destroyed by whatever small time delay there exists in observation. In this paper, we are concerned with a particularly interesting case: Boundary output feedback stabilization of a one-dimensional wave equation system for which the boundary observation suffers from an arbitrary long time delay. We use the observer and predictor to solve the problem: The state is estimated in the time span where the observation is available; and the state is predicted in the time interval where the observation is not available. It is shown that the estimator/predictor based state feedback law stabilizes the delay system asymptotically or exponentially, respectively, relying on the initial data being non-smooth or smooth. Numerical simulations are presented to illustrate the effect of the stabilizing controller.Mathematics Subject Classification. 35B37, 93B52, 93C05, 93C20, 93D15.