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arXiv · 1711.01412

An alternative approach for stability analysis of discrete time nonlinear dynamical systems

Rachid Bouyekhf·Lyubomir T. Gruyitch
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Abstract

The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear discrete-time dynamical systems. The solution is based on the concept of the $\bf G$-functions introduced in this paper. As a result, new necessary and sufficient conditions for asymptotic stability of such systems and an estimation or the exact determination of the asymptotic stability domain of the state $x=0$ are established. Examples are worked out to illustrate the results.

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Rachid Bouyekhf, Lyubomir T. Gruyitch. 2017-11-04. An alternative approach for stability analysis of discrete time nonlinear dynamical systems. https://doi.org/10.1080/10236198.2017.1391239

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