Stabilization of Uncertain Nonlinear Systems via Immersion and Invariance based Sliding Mode Control

This paper introduces a new methodology for stabilization of uncertain nonlinear system using immersion and invariance (I&I) based sliding mode control. The attractivity of the manifold ensures the reflection of the desired system behavior by I&I principle for the nominal system. Higher-order sliding mode of an arbitrary $r^{th}$ order is invoked to replace the stabilizing control law of an output regulator theory to derive the off-the-manifold with completely controlling the disturbance/uncertainties in finite-time. This makes the system more systematic to achieve the equilibrium point asymptotically. Finally, the validation of proposed strategy is tested on a magnetic-levitation system.