Fuzzy observer-based output feedback control design of discrete-time nonlinear systems: An extended dimension approach

Abstract

Recently, previous results of fuzzy observer-based output feedback control design of discrete-time nonlinear systems have been relaxed by using a multi-samples’ method but it is not very mature. This study presents some developments which give a family of feasible solutions to improve the design quality of the recent result. To accomplish this work, an systematic multi-samples’ approach that is parameter-dependent on normalized fuzzy weighting functions on optional multi-samples’ points is presented in the interest of making good use of more helpful information of the discrete-time nonlinear systems. Furthermore, a new Lyapunov function candidate is given to cooperate with the proposed approach while those redundant terms composed of a set of combinations of the t+1 sampled point are removed. As a result of the above efforts, the main defects of the recent result can be overcome and its conservatism is further reduced by an efficient way. In particular, a compromising solution in aspect of not only reducing the conservatism but also suppressing the computational burden is obtained in the special case of m=1. Finally, an illustrative example is given to validate the effectiveness of the approach presented in this study.