Simplifying the Design of Lipschitz Observers by Applying a Novel Batch Pole Assignment Approach

Abstract

Abstract A novel, analytic design method for full state observers of nonlinear Lipschitz systems with their nonlinear term bounded, is considered. In standard procedures, the Lipschitz constant of the nonlinear term imposes strict restrictions on the observer gain matrix stable selection and introduces a further uncertainty in the design, caused by the heuristic manner of this selection. As shown in the paper, when the system nonlinear term is additionally bounded, which is a common situation for many real world systems such as manipulators in robotics and generators in power systems, the Lipschitz constant restriction is fully relaxed. Under these circumstances, a direct design approach is proposed that assigns the observer linear part eigenvalues at a common, specific, negative real position on the left of the system poles. The whole procedure is conducted by simply solving a Lyapunov-type equation that simultaneously constructs the suitable corresponding gain matrix of the observer. The validity of the method and the enhanced observer performance are verified by simulation results conducted on a fundamental power system example.