Observers for 2 × 2 Hyperbolic Systems with Coupled Nonlocal Boundary Condition

This paper is concerned with the problem of designing observers for 2 × 2 hyperbolic systems with coupled nonlocal boundary condition. Two kinds of hyperbolic systems are treated: one is of homodirectional type and the other is of heterodirectional type. The former actually appears when one considers a model of infectious disease. The latter appears when a chaotic PDE system is studied. The features of this paper lie in that the boundary conditions of systems are nonlocal and coupled. For both systems, observers of Luenberger type are constructed by using integral transformations. For homodirectional hyperbolic systems, the design procedure is applied to state estimation of Kermack-McKendrick PDE model with delay. Also, for heterodirectional hyperbolic systems, it is applied to synchronization of chaotic PDE system.