The decomposition property and stability analysis of a class of fuzzy systems (Q2785116)

The authors consider the decomposition of a class of T-S-K type fuzzy systems. By dividing the input space into subspaces, the system under consideration is decomposed into several subsystems which are the simplest fuzzy systems in the corresponding input-subspaces. Based on this decomposition and using the \(S\)-procedure and some piecewise quadratic Lyapunov function, a sufficient condition for global and exponentially asymptotic stability of the original fuzzy system is given in terms of linear matrix inequalities. NEWLINENEWLINENEWLINEThe results obtained improve some known results due to \textit{K. Tanaka} and \textit{M. Sugeno} [Fuzzy Sets Syst. 45, 135-156 (1992; Zbl 0758.93042)], \textit{W. Wang} and \textit{H. Lin} [IEEE Trans. Fuzzy Syst. 7, 53-64 (1999)] and \textit{S. Michio} [ibid. 7, 201-224 (1999)].NEWLINENEWLINENEWLINEAn illustrative example is also given. Some misprints are in the paper, especially in expression (5) giving the formulation of the fuzzy system under discussion.