On the stability of continuous-time T-S model

This paper proposes a new systematic approach to analyze the stability of continuous T-S fuzzy models in case of having 2×2 and symmetric state matrices. A sufficient stability criterion in terms of Lyapunov function candidate is introduced to investigate the global asymptotic stability of T-S models. This criterion is obtained from estimating the spectrum of Hermitian matrices and has the merit that selection of the common positive-definite matrix P is independent of the sub-diagonal entries of the state matrices. It means, for a set of fuzzy models having the same main diagonal state matrices in their subsystems, it suffices to apply the method once. Several examples are given to illustrate the effectiveness of the proposed method.