Robust H∞ control for a class of discrete time fuzzy systems via delta operator approach

In this paper, we investigate a robust H∞ control problem for a class of T–S fuzzy systems with time delays by using delta operator approach. It is known that a better control effect can be obtained by using delta operator approach than using shift operator approach for small sampling periods. Furthermore, the delta operator can unify some previous related continuous and discrete fuzzy systems into fuzzy delta operator system framework. Based on Lyapunov–Krasovskii functionals in delta domain, a new fuzzy H∞ state feedback controller is presented in terms of linear matrix inequalities. Some experiment results of an ball and beam model on a laboratory-scale setup are presented to illustrate the effectiveness and potential for the developed techniques.