Growth conditions for exponential stability of time-varying perturbed systems |
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Authors: | B Ghanmi N Hadj Taieb |
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Affiliation: | Faculty of Sciences of Sfax, Department of Mathematics, University of Sfax, Tunisia, BP 1171, Sfax, Tunisia |
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Abstract: | In this paper, we derive some sufficient conditions for practical uniform exponential stability of time-varying perturbed systems based on Lyapunov techniques, whose dynamics are in general unbounded in time, in the sense that the solutions are uniform stable and converge to a small neighbourhood of the origin. Under quite general assumptions, we first present a new converse stability theorem for a large class of time-varying systems, which will be used to prove certain stability properties of nonlinear systems with perturbation. Therefore, a new Lyapunov function is presented that guarantees practical uniform exponential stability of perturbed systems. Furthermore, some illustrative examples are presented. |
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Keywords: | time-varying perturbed systems Lyapunov theory practical exponential stability |
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