Abstract
In this paper, we present a generalization approach of an algebraic existing method to estimate stability regions for discrete nonlinear polynomial systems of degree 3. The existing method is based on the enlargement of a guaranteed stability region by applying various steps of a proposed algorithm. Its main limitation is that the initial result has only been subsequently developed in a particular case of a single iteration. The stability domain obtained is consequently not the widest one. Our main contribution in this paper is to develop generalized functions that allow the enlargement of the guaranteed stability region after k iterations, for any value of k. A required fundamental tool is developed and consists in a general formula allowing to give the result of the Kronecker power calculation of two matrices sum. The advantages of this generalization are to reach a larger region of asymptotic stability and to improve the existing methods results. Two application examples illustrate the proposed method.
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Communicated by Luz de Teresa.
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Zakhama, R., Hadj Brahim, A.B.B. & Braiek, N.B. Generalization of a stability domain estimation method for nonlinear discrete systems. Comp. Appl. Math. 37, 1130–1141 (2018). https://doi.org/10.1007/s40314-016-0388-7
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DOI: https://doi.org/10.1007/s40314-016-0388-7