T-S Fuzzy Stochastic Bilinear Model and Fuzzy Controller Design Based on Switching Piecewise Lyapunov Functions

Based on a piecewise quadratic Lyapunov function (PQLF), this paper presents stochastic stability analysis and synthesis methods for the discrete time T-S fuzzy bilinear stochastic systems. Two improved stochastic stability conditions have been established. It is shown that the stability in the mean square for T-S fuzzy bilinear stochastic systems can be established if a PQLF can be constructed. Considering the established stability criterion, the controller can be designed, and the closed loop system is asymptotically stable in the mean square sense. An illustrative example is provided to demonstrate the effectiveness of the results proposed in this paper.