A Piecewise Approximation Approach to Nonlinear Systems: Stability and Region of Attraction

This paper discusses piecewise bilinear models and recurrent fuzzy systems as particular classes of dynamic fuzzy systems, which can be dealt with in the same framework due to their structural similarity. As universal approximators, they are capable of representing any continuous nonlinear system dynamics with arbitrary accuracy by means of a rule base. First, basic definitions of both systems are revisited here, and unifying canonical forms are given. Then, a stability criterion is derived for the system classes, which is based on approximating piecewise quadratic Lyapunov functions and formulated in terms of linear matrix inequalities. The main contribution is the demonstration of the stability analysis and estimation of region of attraction by means of these models, outperforming methods reported in the literature.