Regularization of Second Order Sliding Mode Control Systems

The numerical representation of singular systems [1], with index greater than two and inconsistent initial conditions, presents common features with the implementation of higher order sliding motions, [2], [3]. Indeed higher order sliding modes can be viewed as a way to achieve constrained motions, often expressible as an output-zeroing problem after a transient of finite duration [4]. The choice of the sliding output is the first step of a sliding mode design process (e.g. invariance [5]). If the actual control affects the time derivative of the sliding output, starting from a certain order k >= 1 , the corresponding constrained motion, if attainable, is said to be a k-th order sliding motion [6], [7], [8], [9], [10]. The notion of sliding order is equivalent to the one of relative degree [4].