Piecewise output feedback controller synthesis of discrete time fuzzy systems

This paper presents an observer-based output feedback controller design method for discrete time Takagi-Sugeno fuzzy systems, using a discrete time piecewise Lyapunov function. The proposed piecewise output feedback fuzzy controller is made up of a piecewise state feedback fuzzy controller and observer for each subspace. The validity of such a scheme involving the separation principle is verified by a piecewise Lyapunov function. It is shown that the state feedback control laws and observer gains can be obtained by solving a set of linear matrix inequalities (LMI) that is numerically tractable with commercially available software. An example is given to demonstrate the advantage of the proposed method.