Boundary stabilization of distributed parameter systems governed by symmetric linear hyperbolic system using backstepping approach

In this paper, we are concerned with the frequency and time domain behavior of a heat exchanger network system. The system is governed by first-order symmetric hyperbolic linear partial differential equations with spatially varying coefficients. We use a backstepping approach to transform the system into a target system which has arbitrary decay rate. The state feedback is thus designed. It is shown that the original closed-loop system is exponentially stable with given arbitrary decay rate. Then, we construct a collocated boundary observer which only needs measurements on the controlled boundary, and show the convergence of observer estimates. Both results are combined to obtain a collocated output feedback law.