Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence
of Magnitude Saturation
Pascal Morin, Richard M. Murray, Laurent Praly
1998 IFAC Symposium on Nonlinear Control Systems Design (NOLCOS)
Motivated by some recent results on the stabilization of homogeneous systems, we
present a gain-scheduling approach for the stabilization of non-linear systems. Given a
one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show
how the parameter can be rescaled as a function of the state to give a new stabilizing
controller. In the case of homogeneous systems, we obtain generalizations of some existing
results. We show that this approach can also be applied to non-homogeneous systems. In
particular, the main application considered in this paper is to the problem of
stabilization with magnitude limitations. For this problem, we develop a design method for
single-input controllable systems with eigenvalues in the left closed plane.
Conference
Paper (PDF, 433K, 31 pages)
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Richard Murray (murray@cds.caltech.edu)