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Diagonal stability of a class of discrete-time positive switched systems with delay

Diagonal stability of a class of discrete-time positive switched systems with delay

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A class of discrete-time non-linear positive time-delay switched systems with sector-type non-linearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov–Krasovskii (L–K) functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L–K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete-time models of digital filters and neural networks. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.

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