Sliding-mode observers design for singular perturbation systems

The singular perturbation system with inaccessible states is considered. A sliding-mode observer for the system is designed. The separate sliding surfaces of the slow and fast subsystems obtained from the originally full-order system using the concept of manifolds are preselected. The reaching conditions for sliding surfaces of the subsystems are verified with composite control for the full-order system. The error between the closed-loop subsystems response and the actual closed-loop system response is of order O(ε). Finally, an example is exploited to illustrate the theoretic results