Stabilization Analysis for Nonlinear Systems Under Coupled Fuzzy Controller: A Non-PDC Approach

In this study, we present a coupled fuzzy controller design to stabilize a continuous nonlinear system (NS) with external perturbations that are depicted by the Takagi–Sugeno (T–S) fuzzy systems. First, the coupled fuzzy controller is anticipated by incorporating non-parallel distributed compensation (non-PDC) techniques. Then, the proper non-quadratic Lyapunov functional (non-QLF) is taken into account. By employing the time derivatives of non-QLF, Jensen’s inequality techniques, some stabilization conditions are attained in the formulation of linear matrix inequalities to guarantee that the concerned NS is stochastically asymptotically stable together with the $H_{\infty }$ perturbation damping criterion. Finally, two simulation results are discussed to validate and illustrate the viability of the methodologies we have outlined.