Stability of Switched T-S Fuzzy Systems with All Subsystems Unstable

This paper investigates the stability problem of continuous-time switched nonlinear systems without stable subsystems. The Takagi-Sugeno (T-S) fuzzy model is introduced to represent the nonlinear subsystems. Based on a new bounded maximum average dwell time (BMADT) switching approach, an exponential stability condition is derived with a novel time-varying piecewise multiple Lyapunov function approach. Finally, the effectiveness of the established results is illustrated with a numerical example.