Adaptive Observer of One-Sided Lipschitz Nonlinear Systems

Abstract

Aiming to design an adaptive observer for one-sided Lipschitz nonlinear systems, the paper focuses on extensions to the restrictive nature of the Lipschitz continuity condition and the conservativeness of approaches proposed in the past. Main contributions include the following four aspects. Firstly, new sufficient conditions for the existence of observer and asymptotical stability are developed by using an LMI approach, which can be easily solved via standard numerical software. Then, the design scheme presented can cope with the situation where the one-sided Lipschitz constant is unknown, making the complexity of this algorithm reduced significantly compared to almost all existing results. Thirdly, we remove the constraint of quadratic inner-boundedness which is a limitation imposed extensively by the existing works. Finally, by integrating an adaptation law the conservativeness is dropped sharply, which makes the applicable systems larger. In the end, the effectiveness and less conservativeness of results are tested in a series of numerical examples.