New results on the parametric stability of nonlinear systems

  • Authors:

  • V. Sundarapandian

  • Affiliations:

  • Department of Instrumentation and Control Engineering, SRM Engineering College, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur-603 203, Tamil Nadu, India

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2006

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Abstract

In this paper, we derive some new results on the parametric stability of nonlinear systems. Explicitly, we derive a necessary and sufficient condition for a nonlinear system to be locally parametrically exponentially stable at an equilibrium point. We also derive a necessary condition for the nonlinear system to be locally parametrically asymptotically stable at an equilibrium point. Next, we derive some new results on the parametric stability of discrete-time nonlinear systems. As in the continuous case, we derive a necessary and sufficient condition for a discrete-time nonlinear system to be locally parametrically exponentially stable at an equilibrium point. We also derive a necessary condition for the discrete-time nonlinear system to be locally parametrically asymptotically stable at an equilibrium point. We illustrate our results with some classical examples from the bifurcation theory.