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RESEARCH PAPERS

Lyapunov Stability, Semistability, and Asymptotic Stability of Matrix Second-Order Systems

[+] Author and Article Information
D. S. Bernstein, S. P. Bhat

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2118

J. Vib. Acoust 117(B), 145-153 (Jun 01, 1995) (9 pages) doi:10.1115/1.2838656 History: Received October 01, 1994; Online February 26, 2008

Abstract

Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given. These are used to derive several known stability and instability criteria as well as a few new ones. In addition, examples are given to illustrate the stability conditions.

Copyright © 1995 by The American Society of Mechanical Engineers
Topics: Stability , Damping
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