Improvements to the linear differential inclusion approach to stability analysis of linear systems with saturated linear feedback

Ellipsoids, as level sets of quadratic Lyapunov functions, and the convex hull of ellipsoids, as a level set of a certain composite quadratic Lyapunov function, have both been extensively used as estimates of the domain of attraction of a linear system under saturated linear feedback. By expressing...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 49; no. 3; pp. 821 - 828
Main Authors Li, Yuanlong, Lin, Zongli
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.03.2013
Elsevier
Subjects
Actuator saturation
Applied sciences
Attraction
Composite Lyapunov function
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Domain of attraction
Ellipsoids
Exact sciences and technology
Feedback
Hulls
Hulls (structures)
Law
Linear systems
Lyapunov functions
Set invariance
System theory
Domain of attraction
Composite Lyapunov function
Actuator saturation
Set invariance
Saturation
Feedback regulation
Linear condition
Invariant set
Dynamical system
Conservative system
Convex hull
Convex function
Differential inclusion
Ellipsoid
Actuator
Lyapunov function
Quadratic function
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Summary:Ellipsoids, as level sets of quadratic Lyapunov functions, and the convex hull of ellipsoids, as a level set of a certain composite quadratic Lyapunov function, have both been extensively used as estimates of the domain of attraction of a linear system under saturated linear feedback. By expressing the saturated linear feedback law on the convex hull of a group of linear feedback laws, which in turn expresses the linear system under this saturated linear feedback in a linear differential inclusion, conditions have been established under which an ellipsoid or the convex hull of a group of ellipsoids are contractively invariant sets and are thus estimates of the domain of attraction. These conditions are usually less conservative for single input systems than for multiple input systems. In this paper, we consider multiple input systems and establish conditions for contractive invariance of the convex hull of ellipsoids that are less conservative than the existing conditions.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2012.12.002