Backstepping-forwarding boundary control design for first-order hyperbolic systems with Fredholm integrals

In this article, a backstepping-forwarding transform is developed for the boundary stabilization of a class of non-strict feedback first-order hyperbolic systems. Sufficient conditions for the well-posedness of the resulting kernel equations are given, both in terms of the spectrum of some integral operators and, more conservatively, in terms of the magnitude of the coefficients of the system equation. The results presented in this paper reduce to known backstepping results when the non-strict feedback terms are zero.