Observers in the sliding mode control of uncertain nonlinear nonaffine systems with matched and unmatched uncertainties

The paper considers the variable-structure control of nonlinear uncertain nonaffine systems when the state vector is not completely available and the use of observers is required. The strategy of introducing integrators in the input channel is exploited to enlarge the class of tractable control systems. A full-order observer is proposed and conditions are found under which it is proven the convergence to the unique ideal solution of both system and observer. The control problem is solved by forcing a sliding regime for the observer, while satisfying an exponential stability criterion for the observation error state equation.