Stability Analysis of a Multilink Flexible Manipulator: Nonlinear Observers

This paper is concerned with stability analysis problem of nonlinear observer design for a class of multilink flexible manipulators (MLFMs). Specifically, the dynamics of the MLFM is modeled by the use of a Lagrangian approach. In a unified algebraic Riccati matrix equality (ARME) framework, one corresponding error-state system is proven to be asymptotic stable in the mean square (ASMS) for a nonlinear observer design with a known feedback gain; However, since feedback control input is dependent of systematic uncertainty, nonlinear observer design problem with an unknown feedback gain is investigated in the first place. Further, one expansion augment system is proven to remain ASMS in the nonlinear observer design. Therefore, sufficient and necessary conditions of the two desired nonlinear observers can be designed and derived from the developed theory. Finally, simulation studies are used to verify the electiveness of the proposed approach is illustrated by simulation studies.