Reducing the conservatism of stability analysis for discrete-time T-S fuzzy systems based on a delayed Lyapunov function

In this study, we propose some relaxed stability conditions for discrete-time Takagi-Sugeno fuzzy systems. In contrast to existing methods in the literature which are only parameter-dependent on the current-instant normalized fuzzy weighting functions, a delayed Lyapunov function that is formulated in a higher order form of the multi-instant normalized fuzzy weighting functions than existing ones is proposed for achieving the mission of reducing conservatism. It is proved in theory that the method given in this paper includes a recent result in the literature as one special case. Finally, a simulation example is employed to show the effectiveness of the proposed method. HighlightsA new nonquadratic Lyapunov function is proposed.The criterion takes the form of an LMI which is computationally tractable.The obtained stability criteria are less conservative.The existing results are special cases of ours.

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