Strict Lyapunov functions for generating robust oscillations in nonlinear systems
| Authors: | Gomez-Estern Fabio, University of Seville, Spain
Barreiro A., University of Vigo, Spain
Aracil J., University of Seville, Spain
Gordillo F., University of Seville, Spain |
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| Topic: | 2.3 Non-Linear Control Systems |
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| Session: | Control and Chaos |
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| Keywords: | Forced oscillation, Robust control, Lyapunov equation |
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Abstract
This paper deals with the problem ofgenerating stable and robust oscillations in triangular nonlinearsystems. The method consists of two steps. First, a globallyattractive oscillation is induced in a nominal second--ordersubsystem. Based on a partition of the state space and solvingthe Lyapunov equation on each part, a strict Lyapunov functionis obtained that ensures exponential converges to aring--shaped region containing the target limit cycle is madeattractive. Then, the nominal stabilizing controller and therobustness result are extended to arbitrary order systems, via amethod in the essence of backstepping. Moreover, the ability todeal with unmodeled dynamics, extends the applications of theseideas to quasi-triangular structures.
