An LMI approach to H∞ boundary control of semilinear parabolic and hyperbolic systems

Emilia Fridman; Yury Orlov

doi:10.1016/j.automatica.2009.04.026

An LMI approach to H_∞ boundary control of semilinear parabolic and hyperbolic systems

Emilia Fridman, Yury Orlov

School of Electrical Engineering

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

Abstract

Exponential stability analysis and L₂-gain analysis are developed for scalar uncertain distributed parameter systems, governed by semilinear partial differential equations of parabolic and hyperbolic types. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for both systems. These conditions are then utilized to synthesize H_∞ static output feedback boundary controllers of the systems in question.

Original language	English
Pages (from-to)	2060-2066
Number of pages	7
Journal	Automatica
Volume	45
Issue number	9
DOIs	https://doi.org/10.1016/j.automatica.2009.04.026
State	Published - Sep 2009

Keywords

Distributed parameter systems
H control
LMI
Lyapunov functional
Stability

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10.1016/j.automatica.2009.04.026

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abstract = "Exponential stability analysis and L2-gain analysis are developed for scalar uncertain distributed parameter systems, governed by semilinear partial differential equations of parabolic and hyperbolic types. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for both systems. These conditions are then utilized to synthesize H∞ static output feedback boundary controllers of the systems in question.",

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AB - Exponential stability analysis and L2-gain analysis are developed for scalar uncertain distributed parameter systems, governed by semilinear partial differential equations of parabolic and hyperbolic types. Sufficient exponential stability conditions with a given decay rate are derived in the form of Linear Matrix Inequalities (LMIs) for both systems. These conditions are then utilized to synthesize H∞ static output feedback boundary controllers of the systems in question.

KW - Distributed parameter systems

KW - H control

KW - LMI

KW - Lyapunov functional

KW - Stability

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An LMI approach to H_∞ boundary control of semilinear parabolic and hyperbolic systems

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Keywords

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