The SOS-based extended design of polynomial fuzzy control

In recent years, the polynomial fuzzy control becomes a popular research after the Takagi-Sugeno (T-S) fuzzy control. The polynomial fuzzy model is a more effective representation than the T-S fuzzy model. In addition, the stability conditions of polynomial fuzzy control in terms of sum of square (SOS) are more general than the stability conditions of T-S fuzzy control in terms of linear matrix inequality (LMI). This paper provides two extended control designs of polynomial fuzzy control to deal with the issues about how to make the system response converge quickly and how to restrict the system output. To make the system response converge faster, the authors used the concept of decay rate into the polynomial Lyapunov function, and then the new stability conditions are derived. To restrict the system output, the authors proposed the output constraints in terms of SOS via polynomial Lyapunov function. The control feedback gains of polynomial fuzzy controllers can be obtained by solving the above SOS conditions and constraints via SOSTOOLS.