Application of an Estimation Method in the Lure System

The presence of set-valued mapping affects the stability of the output of the lure system, adding to the difficulty in observer design. To overcome the difficulty, the author mapped the system output error to the nonlinear term of the framer, creating a framer of the extended Luenberger structure, and analyzed the coordination of the error system by the monotonic system theory. On this basis, the interval observer was designed for the lure system. Then, the lure system and its observer systems were proved as asymptotically stable. Finally, it is proved that the observer system trajectory always followed the original state trajectory through the simulation under the different selections of set-valued mapping.