Takagi-Sugeno fuzzy regulator design for nonlinear and unstable systems using negative absolute eigenvalue approach

This paper introduces a Takagi-Sugeno (T-S) fuzzy regulator design using the negative absolute eigenvalue (NAE) approach for a class of nonlinear and unstable systems. The open-loop system is initially embodied by the traditional T-S fuzzy model and then, all closed-loop subsystems are combined using the proposed Max-Min operator in place of traditional weighted average operator from the controller side to lessen the coupling virtually and simplify the proposed regulator design. For each virtually decoupled closed-loop subsystem, the composite regulators (i.e., primary and secondary regulators) are designed by the NAE approach based on the enhanced eigenvalue analysis. The Lyapunov function is utilized to guarantee the asymptotic stability of the overall T-S fuzzy control system. The most popular and widely used nonlinear and unstable systems like the electromagnetic levitation system (EMLS) and the inverted cart pendulum (ICP) are simulated for the wide range of the initial conditions and the enormous variation in the disturbance. The transient and steady-state performance of the considered systems using the proposed design are analyzed in terms of the decay rate, settling time and integral errors as IAE, ISE, ITAE, and ITSE to validate the effectiveness of the proposed approach compared to the most popular and traditional parallel distributed compensation (PDC) approach.