<b>Projective Synchronization and</b> H∞ <b>Control of a T-S Fuzzy-Based COVID-19 SEIR Model</b>

This paper addresses the projective synchronization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msub> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞</mml:mi> </mml:msub> </mml:math> control of the Susceptible-Exposed-Infectious-Recovered (SEIR) COVID-19 model using Takagi-Sugeno (T-S) fuzzy control techniques. A fuzzy controller design is proposed to synchronize the SEIR nonlinear model by using the Linear Matrix Inequality (LMI) technique and the Lyapunov function. Based on the LMI technique, Lyapunov function, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞</mml:mi> </mml:msub> </mml:mrow> </mml:math> control theory, the system's stability and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞</mml:mi> </mml:msub> </mml:mrow> </mml:math> performance is ensured by a set of necessary criteria. The advantage of this research lies in its ability to enhance system stability, defined via Lyapunov-based LMI conditions, and robustness, measured through the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞</mml:mi> </mml:msub> </mml:mrow> </mml:math> disturbance attenuation level, both of which are crucial for effective pandemic management. This paper presents simulations and numerical data to highlight the benefits of the proposed method, demonstrating its effectiveness in mitigating the negative consequences of the COVID-19 pandemic by comparing controlled and uncontrolled scenarios.