Switching Fuzzy Model Construction and Controller Design for Dynamical Systems with Input Nonlinearity

Fuzzy model-based control mainly deals with dynamical systems which affinely depend on control inputs. In this paper, dynamical systems which is permitted to have nonlinearity not only in the states, but also in the inputs is considered. Input nonlinearity makes a nonlinear system complicated and makes the number of fuzzy model rules increase. Thus, switching fuzzy control approach is employed. Firstly, the switching fuzzy model construction with arbitrary linear dividing planes, which is an extension of the ordinary switching fuzzy model construction method with dividing planes corresponding to quadrants, is introduced. Secondly, by applying the switching fuzzy model construction method to the dynamical system with input nonlinearity, the switching fuzzy model with membership functions which depend on control inputs is constructed. Finally, by utilizing the dynamic state feedback control approach, we show that membership functions which depend on control inputs can be calculated. Moreover, by employing augmented system approach, the switching fuzzy dynamic state feedback controller design conditions based on the switching Lyapunov function are derived in terms of linear matrix inequalities. A design example illustrates the utility of this approach.