Robust static output-feedback vaccination policy design for an uncertain SIR epidemic model with disturbances: Positive Takagi–Sugeno model approach. (February 2022)

• Record Type: Journal Article
• Authors: Lee, Ho Jae
• Is Part Of: Biomedical signal processing and control. Volume 72(2022)Part A
• Publication Date: 2022-02
• Subjects: Epidemic model -- Takagi–Sugeno (T–S) fuzzy model -- Positive system -- Static output feedback -- L∞–L∞ disturbance attenuation; Signal processing -- Periodicals; Biomedical engineering -- Periodicals; Signal Processing, Computer-Assisted -- Periodicals; Image Processing, Computer-Assisted -- Periodicals; Biomedical Engineering -- Periodicals; 610.28
• DOI: 10.1016/j.bspc.2021.103273
• Languages: English
• ISSNs: 1746-8094

Abstract

Highlights: An analytic vaccination policy using only the inaccurate information of the infected is established for a susceptible-infected-recovered epidemic model based on Takagi-Sugeno (T-S) fuzzy model. The design conditions guarantee that all the state variables of the closed-loop fuzzy model are positive in any time interval. The designed static output-feedback controller also exhibits peak-to-peak disturbance attenuation performance and are robust against norm-bounded parametric uncertainties. The case study for the positive stabilization of the uncertain nonlinear SIR model demonstrates the effectiveness of the proposed methodology. Abstract: An analytic vaccination policy is established for a nonlinear susceptible–infected–recovered (SIR) epidemic model involving uncertainties and disturbances by using only the inaccurate information of the infected through the positive Takagi–Sugeno (T–S) fuzzy approach. The SIR model is exactly represented as the fuzzy model in the T–S form. Two conditions for fuzzy static output-feedback controllers are formulated using the symmetric and diagonal Lyapunov matrices. These controllers exhibit L ∞ – L ∞ disturbance attenuation performance, are robust against norm-bounded parametric uncertainties, and preserve closed-loop positivity. The case study for the positive stabilization of the uncertain nonlinear SIR model demonstrates the effectiveness of the proposed methodology.