NDLI: Partial asymptotic stability and stabilization of nonlinear abstract differential equations

Content Provider	IEEE Xplore Digital Library
Author	Zuyev, A.
Copyright Year	2003
Description	Author affiliation: Inst. of Appl. Math. & Mech., Nat. Acad. of Sci., Ukraine (Zuyev, A.)
Abstract	The problem of partial asymptotic stability with respect to a continuous functional is considered for a class of abstract multivalued systems on a metric space. Such a class includes nonlinear finite and infinite dimensional dynamical systems, differential inclusions, delay equations, etc. An extension of the invariance principle for multivalued dynamical systems is obtained provided that there is a continuous Lyapunov functional. By applying this technique, we derive a sufficient condition for partial asymptotic stability of the equilibrium in a metric space. For dynamical systems on a finite dimensional Euclidean space, the above result is analogous to the Risito-Rumyantsev theorem. The case of nonlinear continuous semigroups on a Banach space is characterized by means of differentiable Lyapunov functionals. Namely, if the above functional is positive definite with respect to a part of the state variables and its time-derivative is non-positive, then the semigroup is partially asymptotically stable under some extra assumptions on the semigroup trajectories. This result can be applied for solving the partial stabilization problem if strong stabilizability of a distributed system is not possible.
Sponsorship	Honeywell Lab. Xerox Nat. Instruments Math Works
Starting Page	1321
Ending Page	1326
File Size	356356
Page Count	6
File Format	PDF
ISBN	0780379241
ISSN	01912216
DOI	10.1109/CDC.2003.1272792
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-12-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Asymptotic stability Differential equations Extraterrestrial measurements Sufficient conditions Mathematics Delay systems Nonlinear equations Mathematical model Manipulators Space vehicles
Content Type	Text
Resource Type	Article

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