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.

A non-monotonic Lyapunov function (NMLF) is deployed to design a robust H 2 fuzzy observer-based control problem for discrete-time nonlinear systems in the presence of parametric uncertainties. The uncertain nonlinear system is presented as a Takagi and Sugeno (T-S) fuzzy model with norm-bounded uncertainties. The states of the fuzzy system are estimated by a fuzzy observer and the control design is established based on a parallel distributed compensation scheme. In order to derive a sufficient condition to establish the global asymptotic stability of the proposed closed-loop fuzzy system, an NMLF is adopted and an upper bound on the quadratic cost function is provided. The existence of a robust H 2 fuzzy observer-based controller is expressed as a sufficient condition in the form of linear matrix inequalities (LMIs) and a sub-optimal fuzzy observer-based controller in the sense of cost bound minimization is obtained by utilising the aforementioned LMI optimisation techniques. Finally, the effectiveness of the proposed scheme is shown through an example.

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