Determination of Stability With Respect to Positive Orthant for a Class of Positive Nonlinear Systems

When dealing with positive nonlinear systems, conventional theory requires too much for the stability of equilibrium points located on the boundary of the positive orthant, which encourages the consideration of stability with respect to the positive orthant . Generalizing this concept to the stabili...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 53; no. 5; pp. 1329 - 1334
Main Authors Hyungbo Shim, Jo, N.H.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.06.2008
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Applied sciences
Attraction
Basin of attraction
Basins
Bifurcation
Boundaries
center manifold theorem
Chemicals
Computer science; control theory; systems
Control theory. Systems
Dealing
Dynamical systems
Exact sciences and technology
Finance
Forward contracts
Jacobian matrices
Jacobians
Kinetic theory
Lyapunov method
Lyapunov stability
Nonlinear dynamics
Nonlinear systems
positive systems
Stability
Stability analysis
System theory
Systems biology
Attraction
Center manifold
Non linear control
Systems theory
Jacobi matrix
Positive system
positive systems
Equilibrium point
Basin of attraction
bifurcation
Non equilibrium conditions
Lyapunov stability
center manifold theorem
Lyapunov function
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Summary:When dealing with positive nonlinear systems, conventional theory requires too much for the stability of equilibrium points located on the boundary of the positive orthant, which encourages the consideration of stability with respect to the positive orthant . Generalizing this concept to the stability of a family of equilibrium points with non-vanishing Basin of attraction (NvBA)-stability has been introduced, which often becomes of interest when positive systems undergo bifurcations. In this technical note, we present a simple condition that can be employed for determining the NvBA-stability with respect to the positive orthant. The proposed condition is applicable to a class of nonlinear systems of certain Jacobian structure and is tailormade for this system. An illustrative example is included in order to help the exposition of the technical note.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2008.921018