Observability analysis of conewise linear systems via directional derivative and positive invariance techniques

Belonging to the broad framework of hybrid systems, conewise linear systems (CLSs) form a class of Lipschitz piecewise linear systems subject to state triggered mode switchings. Motivated by state estimation of nonsmooth switched systems, this paper exploits directional derivative and positive invar...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 46; no. 5; pp. 843 - 851
Main Author Shen, Jinglai
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.05.2010
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Derivatives
Directional derivative
Exact sciences and technology
Hybrid systems
Invariance
Invariants
Joints
Linear systems
Modelling and identification
Observability
Piecewise linear systems
Positive invariance
State estimation
Switching
Directional derivative
Piecewise linear systems
Observability
Positive invariance
Multimodel control
Invariant
Cone
Necessary and sufficient condition
Linear form
Local time
Hybrid system
Nonsmooth analysis
Systems engineering
Optimal trajectory
Lipschitz function
System identification
State estimation
Piecewise linearization
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Summary:Belonging to the broad framework of hybrid systems, conewise linear systems (CLSs) form a class of Lipschitz piecewise linear systems subject to state triggered mode switchings. Motivated by state estimation of nonsmooth switched systems, this paper exploits directional derivative and positive invariance techniques to characterize finite-time and long-time local observability of a general CLS. For the former observability notion, directional derivative results are developed from the simple switching property, and they yield improved observability conditions. For the latter notion, we focus on the case where a nominal trajectory has finitely many switchings. In order to characterize long-time behaviors of the CLS, necessary and sufficient conditions are obtained for the interior of a positively invariant cone. By employing these conditions, we establish connections between finite-time and long-time local observability; underlying positive invariance properties are unveiled.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2010.02.016