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A direct and converse Lyapunov theorem for a nonlinear 2D discrete system described by the Fornasini–Marchesini second model

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Abstract

A direct and converse Lyapunov theorem for an autonomous nonlinear 2D discrete system described by the Fornasini–Marchesini second model has been obtained in this note. The Fornasini–Marchesini second model is re-formulated as a non-linear operator in an infinite-dimensional space, and the Lyapunov theorem is stated and proved in this setup. The result then extended to ND systems with any \(N \ge 2\).

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Correspondence to Shigeru Hanba.

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Hanba, S. A direct and converse Lyapunov theorem for a nonlinear 2D discrete system described by the Fornasini–Marchesini second model. Multidim Syst Sign Process 31, 289–297 (2020). https://doi.org/10.1007/s11045-019-00663-6

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  • DOI: https://doi.org/10.1007/s11045-019-00663-6

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