Stability analysis of nonlinear dynamic system with linear observer for a multilink flexible manipulator

Abstract In this paper, the stability of nonlinear dynamic system for a multilink flexible manipulator (MLFM) is investigated by designing of linear observer to construct a closed-loop system such that for all admissible parameter uncertainties, unknown nonlinearities, and exogenous disturbances input. In a Lagrangian approach, one closed-loop augmented system is unfolded and proven to be asymptotically stable in the mean square (ASMS) by utilizing a Lyapunov theory. Further, if the stability of dynamic closed-loop system of the manipulator is maintained, a desired linear observer will be obtained by solving several algebraic Riccati inequalities. Simulation studies are used to verify the effectiveness of the proposed approach. One of the main contributions of this work is in the derivation of dynamic system stability with a suitable linear observer for the MLFM, based on Lyapunov theory, which: (1) explains physical mechanism for flexible-link movements and dynamics in a Lagrangian approach and (2) sufficient and necessary conditions of the dynamic system stability are derived through seeking the optimal feasible solutions of several algebraic Riccati matrix inequalities.

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