Research Papers

Observability and Distinguishability Properties and Stability of Arbitrarily Fast Switched Systems

[+] Author and Article Information
Najah F. Jasim

Department of Mechanical Engineering,
University of Karbala,
Karbala 56001, Iraq
e-mail: naje76@yahoo.com

It can be shown from the proof of Claim 1 in Ref. [23], p. 220 that properness and positive definiteness of V(x) imply this condition. Here, we just like to highlight this condition explicitly.

The harmonic series is a divergent sequence of numbers in the form {1,12,13,14,...,1n,...} whose terms approach zero and whose sum grows without bound as n gets large.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 17, 2009; final manuscript received April 21, 2013; published online June 27, 2013. Assoc. Editor: Swaroop Darbha.

J. Dyn. Sys., Meas., Control 135(5), 051011 (Jun 27, 2013) (5 pages) Paper No: DS-09-1321; doi: 10.1115/1.4024363 History: Received November 17, 2009; Revised April 21, 2013

This paper addresses sufficient conditions for asymptotic stability of classes of nonlinear switched systems with external disturbances and arbitrarily fast switching signals. It is shown that asymptotic stability of such systems can be guaranteed if each subsystem satisfies certain variants of observability or 0-distinguishability properties. In view of this result, further extensions of LaSalle stability theorem to nonlinear switched systems with arbitrary switching can be obtained based on these properties. Moreover, the main theorems of this paper provide useful tools for achieving asymptotic stability of dynamic systems undergoing Zeno switching.

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Grahic Jump Location
Fig. 1

Spring-damper-mass system




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