Sign propagation: The art behind the methodology of sliding observers

In this paper, the sliding observer-like system is proposed to reveal the nature of the sliding observers. It is demonstrated that, both sliding observer-like system and sliding observer have the property of finite-time convergence. Meanwhile, the unique property of the sign propagation in the sliding observer-like system is evaluated, and the sign propagation rule on the sliding surfaces is formulated. Most importantly, after all states in sliding observer-like system reached and then are maintained on the sliding surfaces, with the existence of the sign propagation property, the sliding observer is equivalent to the sliding observerlike system. Without loss of generality, the concept of the sign propagation is extended to the high-order system. The simulations are conducted to validate the concept of the sign propagation, the finite-time convergence of the sliding observers and the equivalence between the sliding observer and sliding observer like-system on the sliding surfaces.