Local implications of almost global stability
Resumen:
We prove that for autonomous differential equations with the origin as a fixed point, and with at least one eigenvalue with negative real part, we have that the existence of a density function implies local asymptotical stability. We present examples of a system admitting a density function for which the origin is not locally asymptotically stable and an almost globally stable system for which no function is a density function. Keywords: nonlinear systems, asymptotical stability, density functions, almost global stability
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| 2009 | |
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Nonlinear systems Asymptotical stability Density functions Almost global stability |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/38675 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| Sumario: | We prove that for autonomous differential equations with the origin as a fixed point, and with at least one eigenvalue with negative real part, we have that the existence of a density function implies local asymptotical stability. We present examples of a system admitting a density function for which the origin is not locally asymptotically stable and an almost globally stable system for which no function is a density function. Keywords: nonlinear systems, asymptotical stability, density functions, almost global stability |
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