Nonmonotonic observer-based fuzzy controller designs for discrete time T-S fuzzy systems via LMI

In this paper, based on the nonmonotonic Lyapunov functions, a new less conservative state feedback controller synthesis method is proposed for a class of discrete time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems. Parallel distributed compensation (PDC) state feedback is employed as the controller structure. Also, a T-S fuzzy observer is designed in a manner similar to state feedback controller design. The observer and the controller can be obtained separately and then combined together to form an output feedback controller by means of the Separation theorem. Both observer and controller are obtained via solving a sequence of linear matrix inequalities. Nonmonotonic Lyapunov method allows the design of controllers for the aforementioned systems where other methods fail. Illustrative examples are presented which show how the proposed method outperforms other methods such as common quadratic, piecewise or non quadratic Lyapunov functions.