A Less Conservative LMI Condition for Stability of Discrete-Time Systems with Slope-Restricted Nonlinearities

N. S. Ahmad; Joaquin Carrasco; W. P. Heath

doi:10.1109/TAC.2014.2361398

A Less Conservative LMI Condition for Stability of Discrete-Time Systems with Slope-Restricted Nonlinearities

N. S. Ahmad, Joaquin Carrasco, W. P. Heath

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Abstract

Many conditions have been found for the absolute stability of discrete-time Lur’e systems in the literature. It is advantageous to find convex searches via LMIs where possible. In this technical note, we construct two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities. The first condition is derived via Lyapunov theory while the second is derived via the theory of integral quadratic constraints (IQCs) and noncausal Zames–Falb multipliers. Both conditions are related to the Jury–Lee criterion most appropriate for systems with such nonlinearities, and the second generalizes it. Numerical examples demonstrate a significant reduction in conservatism over competing approaches.

Original language	English
Pages (from-to)	1692-1697
Number of pages	6
Journal	I E E E Transactions on Automatic Control
Volume	60
Issue number	6
DOIs	https://doi.org/10.1109/TAC.2014.2361398
Publication status	Published - Jun 2015

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title = "A Less Conservative LMI Condition for Stability of Discrete-Time Systems with Slope-Restricted Nonlinearities",

abstract = "Many conditions have been found for the absolute stability of discrete-time Lur{\textquoteright}e systems in the literature. It is advantageous to find convex searches via LMIs where possible. In this technical note, we construct two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities. The first condition is derived via Lyapunov theory while the second is derived via the theory of integral quadratic constraints (IQCs) and noncausal Zames–Falb multipliers. Both conditions are related to the Jury–Lee criterion most appropriate for systems with such nonlinearities, and the second generalizes it. Numerical examples demonstrate a significant reduction in conservatism over competing approaches.",

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N2 - Many conditions have been found for the absolute stability of discrete-time Lur’e systems in the literature. It is advantageous to find convex searches via LMIs where possible. In this technical note, we construct two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities. The first condition is derived via Lyapunov theory while the second is derived via the theory of integral quadratic constraints (IQCs) and noncausal Zames–Falb multipliers. Both conditions are related to the Jury–Lee criterion most appropriate for systems with such nonlinearities, and the second generalizes it. Numerical examples demonstrate a significant reduction in conservatism over competing approaches.

AB - Many conditions have been found for the absolute stability of discrete-time Lur’e systems in the literature. It is advantageous to find convex searches via LMIs where possible. In this technical note, we construct two less conservative LMI conditions for discrete-time systems with slope-restricted nonlinearities. The first condition is derived via Lyapunov theory while the second is derived via the theory of integral quadratic constraints (IQCs) and noncausal Zames–Falb multipliers. Both conditions are related to the Jury–Lee criterion most appropriate for systems with such nonlinearities, and the second generalizes it. Numerical examples demonstrate a significant reduction in conservatism over competing approaches.

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DO - 10.1109/TAC.2014.2361398

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JF - I E E E Transactions on Automatic Control

IS - 6

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A Less Conservative LMI Condition for Stability of Discrete-Time Systems with Slope-Restricted Nonlinearities

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