A New Approach for Designing Stable Nonlinear bounded-Lipschitz Observers

Abstract

Observer synthesis for nonlinear Lipschitz systems is still an open problem mainly due to the heuristic manner of obtaining the observer gain matrix. The design is constrained with hard stability restrictions typically imposed by the Lipschitz constant. In this paper, it is shown that when the Lipschitz terms are bounded the stability restrictions can be significantly relaxed and an easily implemented design is deployed which enables the observer linear part eigenvalues to be assigned with a desirable real part on the left of the system poles. The asymptotic stability of the estimation-error is guaranteed by employing a Lyapunov-type equation, which is absolutely compatible with the bounded conditions assumed for the nonlinear terms. As it is easily seen, the proposed observer can be directly integrated into a closed-loop system structure with any linear feedback controller capable to stabilize the original system. The validity of this method is verified by implementing the proposed design on a fundamental power system example. The simulation results fully support the theoretical analysis by exhibiting the easy way of the design which allows an enhanced observer-based control performance.