Fuzzy control of non-linear systems using parameter-dependent polynomial fuzzy model

This study investigates the stability of parameter-dependent polynomial-fuzzy-model-based (PDPFMB) control systems. A parameter-dependent polynomial fuzzy model is proposed to represent a non-linear plant. A parameter-dependent polynomial fuzzy controller is then employed to stabilise the non-linear plant. The stability of PDPFMB control systems is investigated using the sum-of-squares (SOS) technique based on a parameter-dependent Lyapunov function candidate. With the consideration of the information of system parameters, parameter-dependent SOS-based stability conditions are obtained to determine the system stability and polynomial feedback gains. A feasible solution to the stability conditions can be obtained numerically using the third-party Matlab toolbox SOSTOOLS. Unlike the membership functions, as the system parameters are not single signed functions, the traditional analysis approach obtaining the stability conditions cannot be applied. Instead, the membership functions and system parameters are considered as symbolic variables for the construction of the parameter-dependent SOS-based stability conditions. A simulation example is given to demonstrate the merits of the proposed approach.