Nonlinear stabilization via control lyapunov measure

Umesh Vaidya, Prashant G. Mehta, Uday V. Shanbhag

Research output: Contribution to journalArticlepeer-review


This paper is concerned with computational methods for Lyapunov-based stabilization of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. The paper poses and solves the co-design problem of jointly obtaining a control Lyapunov measure and a state feedback controller. The computational framework employs set-oriented numerical techniques. Using these techniques, the resulting co-design problem is shown to lead to a finite number of linear inequalities. These inequalities determine the feasible set of the solutions to the co-design problem. A particular solution can be efficiently obtained using methods of linear programming.

Original languageEnglish (US)
Article number5406095
Pages (from-to)1314-1328
Number of pages15
JournalIEEE Transactions on Automatic Control
Issue number6
StatePublished - Jun 2010


  • Lyapunov methods
  • Nonlinear systems
  • Stability

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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