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Global stability and external stability of dynamical systems

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 1997 Italy Publisher:Elsevier BVJournal:Nonlinear Analysis: Theory, Methods & Applications, volume 28, pages 1,167-1,185 (issn: 0362-546X,

Authors: ANDRIANO V.; BACCIOTTI, Andrea; BECCARI G.;

doi: 10.1016/s0362-546x(97)82867-2

handle: 11583/1396686

Global stability and external stability of dynamical systems

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Abstract

The first part of this paper is devoted to systems of ordinary differential equations without inputs. The formal definition of global stability with respect to a region and characterization of global stability is given. Sufficient conditions for global stability in terms of Lyapunov function are obtained. Relationships between global stability and global asymptotic stability are studied. The second part deals with input systems. A definition of uniform bounded-input-bounded-state stability and its characterization in terms of a class of so-called \({\mathcal K}\) functions is given. The properties of local and global input stability are studied. Some applications to triangular systems are given.

Country

Italy

Related Organizations

Instituto Politécnico Nacional
Mexico
Polytechnic University of Turin
Italy

Keywords

Lyapunov function, local and global input stability, Stability of solutions to ordinary differential equations, systems of ordinary differential equations without inputs, Asymptotic properties of solutions to ordinary differential equations, global stability, uniform bounded-input-bounded-state stability, global asymptotic stability

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