NDLI: Impulsive systems triggered by superposed renewal processes

Content Provider	IEEE Xplore Digital Library
Author	Antunes, D. Hespanha, J.P. Silvestre, C.
Copyright Year	2010
Description	Author affiliation: Dept. of Electrical and Computer Eng., University of California, Santa Barbara, CA 93106-9560, USA (Hespanha, J.P.) \|\| Dep. of Electrical Eng. and Computer Science, Instituto Superior Técnico, ISR, 1046-001 Lisboa, Portugal (Antunes, D.; Silvestre, C.)
Abstract	We consider impulsive systems with several reset maps triggered by independent renewal processes, i.e., the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals. Considering linear dynamic and reset maps, we establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one. The result builds upon a stochastic Lyapunov function approach which allows for providing stability conditions in the general case where the dynamic and the reset maps are non-linear. We also prove that the origin of an impulsive system with nonlinear dynamic and reset maps is stable with probability one if the linearization about zero equilibrium is mean exponentially stable, which justifies the importance of studying the linear case. The application of these results is illustrated in the context of networked control systems. The results in this paper permit the analysis of scenarios in which sensors transmit through independent communication links, which introduce independent and identically distributed intervals between transmissions, instead of sharing a single communication link, as considered in a previous work.
Starting Page	1779
Ending Page	1784
File Size	238120
Page Count	6
File Format	PDF
ISBN	9781424477456
ISSN	07431546
e-ISBN	9781424477463
DOI	10.1109/CDC.2010.5717053
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-12-15
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability analysis Sensors Networked control systems Generators Equations Random variables Hafnium
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

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