Title :
A Piecewise Approximation Approach to Nonlinear Systems: Stability and Region of Attraction
Author :
Gering, Stefan ; Eciolaza, Luka ; Adamy, Jurgen ; Sugeno, Michio
Author_Institution :
Inst. of Autom. Control & Mechatron., Tech. Univ. Darmstadt, Darmstadt, Germany
Abstract :
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.
Keywords :
Lyapunov methods; continuous systems; function approximation; fuzzy systems; linear matrix inequalities; nonlinear systems; piecewise polynomial techniques; stability; stability criteria; continuous nonlinear system dynamics; dynamic fuzzy systems; linear matrix inequalities; nonlinear systems; piecewise bilinear model; piecewise quadratic Lyapunov function approximation; recurrent fuzzy systems; region of attraction estimation; rule base; stability analysis; stability criterion; structural similarity; unifying canonical forms; universal approximator; Approximation methods; Fuzzy systems; Lyapunov methods; Nonlinear dynamical systems; Stability criteria; Piecewise Bilinear Systems; Piecewise Quadratic Lyapunov Functions; Piecewise bilinear systems; Recurrent Fuzzy Systems; Region of Attraction; Stability Analysis,; piecewise quadratic Lyapunov functions; recurrent fuzzy systems (RFSs); region of attraction; stability analysis;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2015.2417870