Observer design for a class of nonlinear piecewise systems. Application to an epidemic model with treatment

•This is the first paper that estimates unknown populations for a SEIR-T model.•We transform considered system into an extended nonlinear observer normal form.•This form allows us to apply a high gain observer to provide global estimations.

Susceptible Exposed Infectious and Recovered epidemic model endowed with a treatment function (SEIR-T model) is a well-known model used to reproduce the behavior of an epidemic, where the susceptible population and the exposed population need to be estimated to predict and control the propagation of a contagious disease. This paper focuses on the nonlinear observer design for a class of nonlinear piecewise systems including SEIR-T models. For this purpose, two changes of coordinates are provided to transform the considered systems into an extended nonlinear observer normal form, on which a high gain observer can be applied. Then, the proposed method is applied to a SEIR-T model. Finally, simulation results are given to show its efficiency.