Lyapunov functions for generalized discrete-time multivariable Popov criterion

N.S. Ahmad; W.P. Heath; G. Li

doi:10.3182/20110828-6-IT-1002.00402

Lyapunov functions for generalized discrete-time multivariable Popov criterion

N.S. Ahmad
, W.P. Heath
, G. Li

University of Exeter
University of Manchester

Research output: Contribution to journal › Article › peer-review

Abstract

This paper shows the existence of Lur'e-Postkinov Lyapunov functions for the generalized multivariable discrete-time Popov criterion. The nonlinearities in the Lur'e system considered here are monotonic, sector- and slope-restricted. We discuss the cases where the nonlinearities are diagonal and non-diagonal. Our derivation is based on the discrete-time Kalman-Yakubovich-Popov (KYP) lemma and the S-Procedure, and results in Linear Matrix Inequality (LMI) conditions which can be solved using convex optimization methods.

Original language	Unknown
Pages (from-to)	3392-3397
Number of pages	6
Journal	IFAC Proceedings Volumes (IFAC-PapersOnline)
Volume	44
Issue number	1
Early online date	1 Jan 2011
DOIs	https://doi.org/10.3182/20110828-6-IT-1002.00402
Publication status	Published - 25 Apr 2016
Externally published	Yes

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10.3182/20110828-6-IT-1002.00402

Cite this

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abstract = "This paper shows the existence of Lur'e-Postkinov Lyapunov functions for the generalized multivariable discrete-time Popov criterion. The nonlinearities in the Lur'e system considered here are monotonic, sector- and slope-restricted. We discuss the cases where the nonlinearities are diagonal and non-diagonal. Our derivation is based on the discrete-time Kalman-Yakubovich-Popov (KYP) lemma and the S-Procedure, and results in Linear Matrix Inequality (LMI) conditions which can be solved using convex optimization methods.",

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