Design of a Global Sliding Mode Controller Using Hyperbolic Functions for Nonlinear Systems and Application in Chaotic Systems

In this research, an LMI-based global sliding mode controller law with a novel switching function for the sliding surface using hyperbolic functions is presented and is used for stabilization and robustness of three-dimensional nonlinear systems with uncertainty. The asymptotic stability of the system's state variables is guaranteed by Linear Matrix Inequality (LMI) and furthermore, considering the uncertainty and nonlinear terms, the reaching phase of the sliding surface is deleted. Finally, the proposed control technique is implemented on Genesio-Tesi chaotic system and the results of the simulation are analyzed.