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Global stability of Clifford-valued Takagi-Sugeno fuzzy neural networks with time-varying delays and impulses

In this study, we consider the Takagi–Sugeno (T-S) fuzzy model to examine the global asymptotic stability of Cliﬀord-valued neural networks with time-varying delays and impulses. In order to achieve the global asymptotic stability criteria, we design a general network model that includes quaternion-, complex-, and real-valued networks as special cases. First, we decompose the n -dimensional Cliﬀord-valued neural network into 2 m n -dimensional real-valued counterparts in order to solve the noncommutativity of Cliﬀord numbers multiplication. Then, we prove the new global asymptotic stability criteria by constructing an appropriate Lyapunov-Krasovskii functionals (LKFs) and employing Jensen’s integral inequality together with the reciprocal convex combination method. All the results are proven using linear matrix inequali-ties (LMIs). Finally, a numerical example is provided to show the eﬀectiveness of the achieved results.