Fast convergence for tracking problem of nth degree system by sliding mode control

The main objective of the paper is to develop sliding mode control (SMC) for tracking problem of continuous nth degree nonlinear system in the form; x⁽ⁿ)(t)=f(x(t))+u(t), where f(x(t)) is a nonlinear function with an uncertainty having a known bound and x(t)=[x(t)x˙(t)...x^(n-1/)(t)]sup T/ is the state vector. A modification of the conventional switching control is proposed which is shown to give fast convergence in the reaching mode without affecting the desired performance in the sliding mode