Relaxed H∞H∞ control design of discrete-time Takagi–Sugeno fuzzy systems: A multi-samples approach

• A novel fuzzy H∞H∞ controller is proposed.
• The criterion takes the form of an LMI which is computationally tractable.
• The obtained design conditions are less conservative.
• The existing results are special cases of ours.

This paper investigates the problem of fuzzy H∞H∞ control design for a class of discrete-time nonlinear control systems via a multi-samples approach. A new fuzzy H∞H∞ controller, which is parameter-dependent on not only the current-time but also the one-step-past membership functions, is developed to derive less conservative design conditions for ensuring both the asymptotic stability and the prescribed H∞H∞ performance index of the obtained closed-loop system. Thanks to the usage of both a new fuzzy Lyapunov function and an extension of the homogenous matrix polynomial methodology, linear matrix inequality (LMI)-based H∞H∞ control design conditions are obtained for minimizing the normal level in a systematic and relaxed way. In addition, further efforts are made by developing an efficient slack variable approach. Finally, two numerical examples are provided to illustrate the effectiveness of the results given in this paper.