Invariance Principles for Hybrid Systems With Connections to Detectability and Asymptotic Stability

This paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural prope...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2007-12, Vol.52 (12), p.2282-2297
Main Authors: Sanfelice, R.G., Goebel, R., Teel, A.R.
Format: Article
Language:English
Subjects:
Applied sciences
Asymptotic properties
Asymptotic stability
Automatic control
Computer science
control theory
systems
Control systems
Control theory. Systems
Convergence
detectability
Exact sciences and technology
Feedback
graphical convergence
Hybrid systems
Initial conditions
Invariance
invariance principles
Joints
Mathematical model
Military computing
Modelling and identification
Noise robustness
Observability
Power system modeling
Robust control
Stability
Vehicle dynamics
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Summary:This paper shows several versions of the (LaSalle's) invariance principle for general hybrid systems. The broad framework allows for nonuniqueness of solutions, Zeno behaviors, and does not insist on continuous dependence of solutions on initial conditions. Instead, only a mild structural property involving graphical convergence of solutions is posed. The general invariance results are then specified to hybrid systems given by set-valued data. Further results involving invariance as well as observability, detectability, and asymptotic stability are given.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2007.910684