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Nonlinear Stabilization via Control Lyapunov Measure

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3 Author(s)
Vaidya, U. ; Dept. of Electr. & Comput. Eng., Iowa State Univ., Ames, IA, USA ; Mehta, P.G. ; Shanbhag, U.V.

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:55 ,  Issue: 6 )

Date of Publication:

June 2010

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