Flexible Robust Control Strategy for Synchronization of Uncertain Non-Linear Systems with Control Input Non-Linearity

A robust global fuzzy sliding mode controller is designed in this paper for the synchronization of non-linear systems with control input non-linearities (CIN) and uncertainties. A consistent global fuzzy sliding mode control (GFSMC) law is developed, which guarantees the suppression of the reaching phase and the presence of the sliding phase from the initial time. Chattering phenomenon, which is characteristic of customary sliding mode control (SMC), avoided by the on-line fuzzy regulation of the sliding surface in the controller, when the system is subject to disturbances and CIN. Finite-time boundedness (FTB) properties are designed with adequate conditions, which are entrenched in terms of linear matrix inequalities (LMIs) with the help of cost and Lyapunov functions. Numerical simulations for the synchronization problem of the chaotic modified Colpitt’s system and Duffing system clearly show the good performance of the proposed control scheme. The present work provides a regular procedure to design GFSMC for a class of non-linear systems with CIN.