A New Approach to Sliding Observer Design and Stability for Linear System

The sliding observer, first introduced by Slotine in mid-1980s, is explored in details from the viewpoint of machine learning. A monarchacial forced learning concept that consists of a leading system and multiple followers is introduced to the named observer. In the learning process, the leader acts as a role model, which exhibits finite convergence property, for the followers to learn. By employing the weighted switching functions in each of the followers' subsystem, forced learning allows the followers to imitate the leader's convergence behaviour, thus, achieving their respective finite-time convergence. On the basis of this concept, a new design method, which greatly simplifies the process of sliding observer design, is proposed by adopting the idea of mapping functions in conjunction with Lyapunov stability theorem. Of the utmost importance, this method proves the existence of finite-time convergence property in the sliding observer as a whole. Numerical examples are presented to verify the theoretical analysis.