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Absolute stability analysis for negative-imaginary systems
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DOI：10.1016/j.automatica.2016.01.029.png)
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Abstract
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This paper deals with absolute stability of a Lur'e system with positive feedback where the linear subsystem exhibits negative-imaginary frequency response and the nonlinearity connected in feedback is time-invariant, memoryless and slope-restricted. The proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative-imaginary class. Along with that, positive definiteness of a symmetric matrix needs to be ensured, where the symmetric matrix is obtained by subtracting the dc-gain matrix of the linear subsystem from a strictly positive diagonal matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities. The stability criterion is proved using a Lure-Postnikov-type Lyapunov function. Numerical examples are presented to demonstrate the proposed results. (C) 2016 Elsevier Ltd. All rights reserved.
Keywords:
Lur'e system
Slope-restricted nonlinearity
Absolute stability
Negative-imaginary system
Positive feedback
Lyapunov function
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