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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 66, Issue 1
  • July 1969, pp. 115-117

Quadratic Lyapunov functions for linear systems

  • Y. V. Venkatesh (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100044777
  • Published online: 24 October 2008
Abstract
Abstract

The paper deals with the existence of a quadratic Lyapunov function V = x′P(t)x for an exponentially stable linear system with varying coefficients described by the vector differential equation The derivative dV/dt is allowed to be strictly semi-(F) and the locus dV/dt = 0 does not contain any arc of the system trajectory. It is then shown that the coefficient matrix A(t) of the exponentially stable system is not identically equal to a unit matrix multiplied by a scalar. The result subsumes that of Lehnigk(1).

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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