On observer-based control of one-sided Lipschitz systems

This paper describes the novel observer-based controller design for the one-sided Lipschitz nonlinear systems. An observer-based controller design condition is obtained by application of the Lyapunov theory, by involving the one-sided Lipschitz condition and quadratic inner-boundedness criterion, an...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2016-03, Vol.353 (4), p.903-916
Main Authors: Ahmad, Sohaira, Rehan, Muhammad
Format: Article
Language:English
Subjects:
Controllers
Decoupling
Design analysis
Design engineering
Dynamical systems
Gain
Mathematical models
Nonlinear dynamics
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Summary:This paper describes the novel observer-based controller design for the one-sided Lipschitz nonlinear systems. An observer-based controller design condition is obtained by application of the Lyapunov theory, by involving the one-sided Lipschitz condition and quadratic inner-boundedness criterion, and by incorporating the matrix inequality procedures. Further, a decoupling condition, necessary and sufficient for the main design approach, is developed to determine the controller and observer gains. Furthermore, two design conditions, a computationally simple sufficient condition and a more generic necessary and sufficient condition, based on the existing and the novel treatments for the one-sided Lipchitz nonlinearity are evaluated to obtain the observer-based control solution. An algorithm for solving the proposed design constraints by combining a nested bilinear-terms-solver approach and a nonlinear-optimization-based cone complementary linearization method is provided. The effectiveness of the proposed observer-based controller design for the one-sided Lipschitz nonlinear systems is demonstrated using a numerical example.
ISSN:0016-0032
1879-2693
DOI:10.1016/j.jfranklin.2016.01.010