This paper presents new stability and stabilisation conditions in the form of linear matrix inequalities for discrete-time Takagi-Sugeno fuzzy systems; they are derived considering a class of non-quadratic Lyapunov functions with multi-parametric non-monotonic terms, which significantly enhances the feasibility set of current state-of-the-art results. In addition, extensions to cope with the disturbance attenuation control problem are included. Benchmark numerical examples are provided to illustrate the effectiveness of the proposed approach.
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