A new fuzzy adaptive law with leakage

In this paper a novel adaptive law with leakage is presented. It is shown in the paper that the proposed adaptive law is a natural way to cope with the parasitic dynamics. Moreover, the value of the leakage parameter σ́ is directly related to the norm of the parasitic dynamics. This is the unique property of the proposed adaptive law since this is not the case when using σ-modification, switching σ-modification, or e1-modification. The boundedness of estimated parameters, the tracking error and all the signals in the system is proven if the leakage parameter σ́ satisfies certain condition. This means that the proposed adaptive law ensures the global stability of the system. A simulation example is given that illustrates the proposed approach.