Infinite-dimensional sliding mode observer analysis for a disturbed linear reaction-convection-diffusion model (Q6137824)

Considering the previous work of \textit{H. Dimassi} et al. [Syst. Control Lett. 124, 40--48 (2019; Zbl 1408.93038)], significant improvements and an in-depth complementary analysis are proposed in this paper. A simplified discontinuous input applied to the error dynamics is presented to the observer model, so that the on-line calculation of the boundary state time derivative is no longer necessary. It is proposed an abstract representation of the state observer and a special attention is granted to its well-posedness on a Sobolev space despite the discontinuity. By considering one boundary measurement and a continuous approximation of the discontinuous input, the exponential stability of the error dynamics is established. Some numerical simulations illustrate the presented results.