This paper concerns the analysis of transferring stability properties from an invariant manifold to the whole space for an ordinary differential system. In previous papers we already treated this problem in the case of asymptotic and total stability. Here we deal with the case of non-asymptotic stability. We generalize to differential systems depending on time a reduction principle [Kelley in J. Math. Anal. 18:336-344, 1967; Pliss in Izv.Nauk SSSR Mat Ser 28:1297-1324, 1964)] relative to autonomous systems. Our procedure is very different from the fixed point theorem argument used in [Kelley in J. Math. Anal. 18:336-344, 1967], and it is based on the use of a suitable Liapunov function. Some results concerning integral stability are also given.
Non-asymptotic stability and integral stability trough a reduction principle / Luigi, Salvadori; Visentin, Francesca. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 63:2(2014), pp. 335-345. [10.1007/s11587-014-0185-9]
Non-asymptotic stability and integral stability trough a reduction principle
VISENTIN, FRANCESCA
2014
Abstract
This paper concerns the analysis of transferring stability properties from an invariant manifold to the whole space for an ordinary differential system. In previous papers we already treated this problem in the case of asymptotic and total stability. Here we deal with the case of non-asymptotic stability. We generalize to differential systems depending on time a reduction principle [Kelley in J. Math. Anal. 18:336-344, 1967; Pliss in Izv.Nauk SSSR Mat Ser 28:1297-1324, 1964)] relative to autonomous systems. Our procedure is very different from the fixed point theorem argument used in [Kelley in J. Math. Anal. 18:336-344, 1967], and it is based on the use of a suitable Liapunov function. Some results concerning integral stability are also given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
