A Direct Pole Placement-based Approach for the Design of Nonlinear Lipschitz Observers

An analytic method for designing full state observers for nonlinear Lipschitz systems is presented in this paper. The method is capable to accommodate the observer linear part pole-assignment requirements with the Lipschitz constant constraints. It is remarkable that the proposed design approach is easily implemented while in many cases can result in even more simplifications. The whole analysis is conducted by simply solving a Lyapunov-type equation that achieves both: to guarantee the observer global asymptotic stability and simultaneously to construct the corresponding gain matrix of the observer. The validity of the method is examined on an onelink manipulator system driven by a dc motor. The simulation results fully verify the theoretical analysis, while when these are compared with those obtained by using conventional LMI techniques, clearly indicate an improved performance.