The Stability of a Second Order Linear Periodic System

[+] Author and Article Information
E. J. Davison

Department of Electrical Engineering, University of Toronto, Toronto, Canada

J. Basic Eng 91(2), 207-210 (Jun 01, 1969) (4 pages) doi:10.1115/1.3571064 History: Received August 02, 1968; Online November 03, 2011


Necessary and sufficient conditions are obtained for the stability of the following second order linear system:

ẋ = θ(t)x,   θ(t) = θt+i=1lTi
θ(t)  = A1,   0<t<T1
  = A2,   T1<t<T1+T2
  = Al,   i=1l−1Ti<t<i=1lTi
in terms of the eigenvalues and elements of the matrices A i , i = 1, 2[[ellipsis]]l. The conditions become very simple for the case that l = 2. An example of a pendulum with a vibrating support is included.

Copyright © 1969 by ASME
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