Sliding surface design for singularly perturbed systems

The equilibrium manifold of a singularly perturbed system has a close relationship with the sliding surface of a variable structure system. The fast time and slow time responses has a similar behavior to the “reaching mode” and “sliding mode”, respectively. This paper aims to equip the powerful composite control method with robustness through variable structure control design. The major bridge in between is a Lyapunov function. It is found that a singularly perturbed system in sliding mode may preserve two-time-scale attribute, in which a new equilibrium manifold exists on the sliding surface. Sliding motions being attracted to the manifold can therefore be referred to as “sliding mode in sliding mode”