Robust observer-based output-feedback control for epidemic models: Positive fuzzy model and separation principle approach

Abstract

A feedback-type vaccination and treatment policy for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances is designed by considering only the number of infected individuals. Specifically, an observer-based output-feedback (OBOF) controller design methodology in the Takagi–Sugeno fuzzy model framework is established. The designed controller exhibits L∞–L∞ disturbance attenuation performance, is robust against norm-bounded parametric uncertainties, and can preserve the closed-loop positivity. The primary contributions of the proposed design condition can be characterized as follows: (i) a novel structure of a fuzzy OBOF controller to ensure the closed-loop positivity; (ii) separate disturbance attenuation performances for the independent design of the controller and observer; (iii) The independent design conditions formulated as convex optimization problems in the presence of parametric uncertainties; (iv) the demonstration of the separation principle in the positive L∞–L∞ disturbance attenuation problem. Results of the case study pertaining to the SIR model demonstrate the efficacy of the proposed methodology.