Introduction

Abstract

This part considers systems in the form (1.20), consisting of a single first order linear hyperbolic PIDE, with local and non-local reaction terms, and with scaled actuation and anti-collocated measurement. These can be stated as

$$u_t(x, t) - \lambda (x) u_x(x, t) = f(x) u(x, t) + g(x) u(0, t)$$

$$\qquad \qquad + \int _{0}^{x} h(x, \xi ) u(\xi , t) d\xi $$

$$u(1, t) = k_1 U(t)$$

$$u(x, 0) = u_0(x)$$

$$y(t) = k_2 u(0, t)$$