Sliding mode control based on observers for uncertain nonlinear systems

The paper considers uncertain nonlinear nonaffine systems affected by matched and unmatched uncertainties. The state of the system is not accessible, while a a possibly nonlinear output is available. Integrators are introduced in the input channel and the first time derivative of the original control is regarded as the new control. The obtained augmented system satisfies a convexity condition. A full-order observer is designed and the control problem is solved by steering the observer to the sliding manifold. While this sliding motion is maintained, conditions are found under which it is proven the exponential stability of the observation error. Furthermore both system and observer are proven to converge to the unique ideal solution.