Stability analysis for a class of functional differential equations and applications
The problem of Lyapunov stability for functional differential equations in Hilbert spaces is studied. The system to be considered is non-autonomous and the delay is time-varying. Known results on this problem are based on the Gronwall inequality yielding relative conservative bounds on nonlinear per...
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th-cmuir.6653943832-597152018-09-10T03:20:25Z Stability analysis for a class of functional differential equations and applications V. N. Phat P. Niamsup Mathematics The problem of Lyapunov stability for functional differential equations in Hilbert spaces is studied. The system to be considered is non-autonomous and the delay is time-varying. Known results on this problem are based on the Gronwall inequality yielding relative conservative bounds on nonlinear perturbations. In this paper, using more general Lyapunov-Krasovskii functional, neither model variable transformation nor bounding restriction on nonlinear perturbations is required to obtain improved conditions for the global exponential stability of the system. The conditions given in terms of the solution of standard Riccati differential equations allow to compute simultaneously the two bounds that characterize the stability rate of the solution. The proposed method can be easily applied to some control problems of nonlinear non-autonomous control time-delay systems. © 2009 Elsevier Ltd. All rights reserved. 2018-09-10T03:20:25Z 2018-09-10T03:20:25Z 2009-12-15 Journal 0362546X 2-s2.0-72149124470 10.1016/j.na.2009.06.028 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=72149124470&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/59715 |
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Mathematics V. N. Phat P. Niamsup Stability analysis for a class of functional differential equations and applications |
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The problem of Lyapunov stability for functional differential equations in Hilbert spaces is studied. The system to be considered is non-autonomous and the delay is time-varying. Known results on this problem are based on the Gronwall inequality yielding relative conservative bounds on nonlinear perturbations. In this paper, using more general Lyapunov-Krasovskii functional, neither model variable transformation nor bounding restriction on nonlinear perturbations is required to obtain improved conditions for the global exponential stability of the system. The conditions given in terms of the solution of standard Riccati differential equations allow to compute simultaneously the two bounds that characterize the stability rate of the solution. The proposed method can be easily applied to some control problems of nonlinear non-autonomous control time-delay systems. © 2009 Elsevier Ltd. All rights reserved. |
| format |
Journal |
| author |
V. N. Phat P. Niamsup |
| author_facet |
V. N. Phat P. Niamsup |
| author_sort |
V. N. Phat |
| title |
Stability analysis for a class of functional differential equations and applications |
| title_short |
Stability analysis for a class of functional differential equations and applications |
| title_full |
Stability analysis for a class of functional differential equations and applications |
| title_fullStr |
Stability analysis for a class of functional differential equations and applications |
| title_full_unstemmed |
Stability analysis for a class of functional differential equations and applications |
| title_sort |
stability analysis for a class of functional differential equations and applications |
| publishDate |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=72149124470&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/59715 |
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