Lyapunov functions for discrete-time multivariable Popov criterion with indefinite multipliers

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

doi:10.1109/CDC.2010.5717085

Lyapunov functions for discrete-time multivariable Popov criterion with indefinite multipliers

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

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper shows the existence of Lur'e-Postkinov type Lyapunov functions for the discrete-time multivariable Popov criterion with indefinite multipliers. The nonlinearities in the Lur'e systems considered here are monotonic, sector- and slope-restricted. We discuss the case where the nonlinearities are 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
Number of pages	6
DOIs	https://doi.org/10.1109/CDC.2010.5717085
Publication status	Published - 22 Feb 2011
Externally published	Yes
Event	49th IEEE Conference on Decision and Control (CDC) - Atlanta, United States Duration: 15 Dec 2010 → 17 Dec 2010

Conference

Conference	49th IEEE Conference on Decision and Control (CDC)
Country/Territory	United States
City	Atlanta
Period	15/12/10 → 17/12/10

Access to Document

10.1109/CDC.2010.5717085

Cite this

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title = "Lyapunov functions for discrete-time multivariable Popov criterion with indefinite multipliers",

abstract = "This paper shows the existence of Lur'e-Postkinov type Lyapunov functions for the discrete-time multivariable Popov criterion with indefinite multipliers. The nonlinearities in the Lur'e systems considered here are monotonic, sector- and slope-restricted. We discuss the case where the nonlinearities are 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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N2 - This paper shows the existence of Lur'e-Postkinov type Lyapunov functions for the discrete-time multivariable Popov criterion with indefinite multipliers. The nonlinearities in the Lur'e systems considered here are monotonic, sector- and slope-restricted. We discuss the case where the nonlinearities are 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

AB - This paper shows the existence of Lur'e-Postkinov type Lyapunov functions for the discrete-time multivariable Popov criterion with indefinite multipliers. The nonlinearities in the Lur'e systems considered here are monotonic, sector- and slope-restricted. We discuss the case where the nonlinearities are 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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