A Backstepping Method for Controlling a Nonlinear System of Fuzzy Delay Differential Equations

This paper presents a control strategy for a nonlinear system of fuzzy delay differential equations (FDDEs) using the generalizable backstepping method (GBSM). Despite the inherent challenges posed by uncertain parameters and time delays, this method successfully achieves system stability at specific time intervals using the general functions of control which have been created based on the Lyapunov function. Additionally, the method of successive integrations is employed to transform the original FDDEs system into an equivalent system of fuzzy differential equations (FDEs), facilitating the application of the GBSM. Finally, substitution the control functions in the transformed system (FDEs) in final step that leads to a new system is an exponentially stable. As a result, the proposed control strategy for stabilizing FDDEs has been effectively demonstrated by numerical simulation (MATLAB and Mathcad platforms).