Sampled-data controllers and observer-design for uncertain semilinear systems with positivity constraints

Abstract

This paper deals with the problem of positive stabilization of a class of uncertain semilinear diffusion systems using sampled-data controllers. The conditions for the existence of such controllers are obtained through certain inequalities. By solving these inequalities, we determine upper bounds for the sampling intervals that guarantee exponential stability, as well as the corresponding decay rates. Furthermore, the design of a positive observer for systems with discrete measurements is studied. The stability of the estimation error is ensured through the same LMIs. Numerical simulations are presented to illustrate the effectiveness of the proposed approach.