Stability of a Class of Evolving Fuzzy Systems

In this chapter, we introduce the stability proof of a class of EFSs which are comprised of the structure learning and the recursive least squares parameter update method, such as EFS based on data clouds, eTS [1], Simpl \(\_\) eTS [2], ESAFIS, AnYa using eClustering [3] and so on. The stability of the class of EFSs is proven through the Lyapunov theory, and the proof of stability shows that the average identification error converges to a small neighborhood of zero. The stability performance is verified through the EFS based on data clouds and some numerical examples. The simulation results also demonstrate that the average error is bounded and converges to a small neighborhood of zero.