International audienceAn integral transform is introduced which allows the construction of boundary controllers and observers for a class of first-order hyperbolic PIDEs with Fredholm integrals. These systems do not have a strict-feedback structure and thus the standard backstepping approach cannot be applied. Sufficient conditions for the existence of the backstepping-forwarding transform are given in terms of spectral properties of some integral operators and, more conservatively but easily verifiable, in terms of the norms of the coefficients in the equations. An explicit transform is given for particular coefficient structures. In the case of strict-feedback systems, the procedure detailed in this paper reduces to the well-known backstepping design. The results are illustrated with numerical simulations

In this paper, we consider the problem of L 2exponential stabilization of a coupled ODE-hyperbolic PDE-ODE system, where actuation is available through one ODE.Based on the backstepping technique, the system is mapped into an equivalent delay form which allows for the construction of a strictly proper controller realized as a full-state feedback. The result extends previous control designs, lifting some restrictions on the structure of the ODEs under consideration and guaranteeing a non-zero delay margin for the closed-loop system.

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In this paper, we study the problem of stabilizing a linear ordinary differential equation through a system of an n + m (hetero-directional) coupled hyperbolic equations in the actuating path. The method relies on the use of a backstepping transform to construct a first feedback to tackle in-domain couplings present in the PDE system and then on a predictive tracking controller used to stabilize the ODE. The proposed control law is robust with respect to small delays in the control signal.

We consider the problem of full-state feedback stabilization of a (possibly unstable) system of hyperbolic partial differential equations (PDEs). Unlike previous works, boundary couplings to linear ordinary differential equations (ODEs) at both boundaries are considered and actuation is available through one of these ODE dynamics. This structure can arise when considering linear (or linearized) systems of balance laws with finite-dimensional actuator and load dynamics. The feedback law proposed in this paper is constructed using an invertible transform based on the (infinite-dimensional) backstepping method.