Dynamical sliding mode control of perturbed nonlinear systems in strict feedback form

We consider high order sliding mode control of SISO nonlinear systems, perturbed by bounded and unmatched disturbances. The systems are assumed to be in strict-feedback form. Design of the sliding surface dynamics and reaching dynamics are achieved via lower triangular state transformations with full state feedback. The state transformations are simply modifications of those obtained via the backstepping algorithm. The notation used here provides clear insight into how the backstepping algorithm works from a structural viewpoint. A smooth, dynamic control law is determined such that the system is forced arbitrarily close to the sliding surface. Lyapunov analysis shows that the system is robustly stable.