Observer design for n + m linear hyperbolic ODE-PDE-ODE systems

International audienceIn this paper, an observer design is presented for a system of n+m hetero-directional transport partial differential equations (PDEs) coupled on both boundaries of the domain to ordinary differential equations (ODEs). This class of systems can represent, for instance, actuator and load dynamics at the boundaries of a hyperbolic system. The results in this paper provide a constructive way to reconstruct the state of the ODEs and the PDEs using only available measurements on one of the two ODEs. This observer design completes existing fullstate feedback designs for this class of systems and enables, together with previous results, the construction of outputfeedback stabilizers. As a complementary result, this paper includes a simple (constructive) method to obtain a stable leftinverse of a specific transfer matrix required in the observer design, which can also be applied (after a transposition) to the computation of the analogous stable right-inverses required for the control design