A survey on stability research of discrete-time Takagi-Sugeno fuzzy control systems

The development of the stability research on Takagi-Sugeno (T-S) fuzzy control is surveyed in this paper. For the first time, this paper distinguishes between the single layer fuzzy summation and the double layer fuzzy summation, where the latter improves the former at least for the discrete-time systems. For the first time, this paper distinguishes between the first stage approximation and the second stage approximation, where the latter improves the former by applying the techniques of the homogeneous polynomials. At least for the discrete-time systems, the stabilization can be achieved by applying the homogeneously polynomially parameterized control law and checking through the homogeneously polynomially parameterized Lyapunov functions, if and only if the stabilization can be achieved by applying any continuously parameterized control law and checking through the continuously parameterized Lyapunov functions.