Stability analysis and output feedback control for a class of switched nonlinear systems

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The problem of stability analysis and output feedback control for a class of switched nonlinear systems is addressed in this paper. The subsystems are from the class of so-called Φ-systems (σ-systems). The standard saturation and the hyperbolic tangent (popular activation function in neural networks) are examples of this type of nonlinearity. The discrete-time recurrent artificial neural network is a special case of Φ-systems. Furthermore, results related to this class of nonlinear systems have potential applications in the classical problems related to uncertain nonlinearities such as Lure systems. Two linear matrix inequality-based (LMI) sufficient conditions for asymptotic stability are proposed for these switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. Two conditions for output feedback controller synthesis based on the proposed stability conditions are presented. The results are further illustrated by numerical examples.
Original languageEnglish
JournalInternational Journal of Modelling, Identification and Control
Volume22
Issue number4
ISSN1746-6172
DOIs
Publication statusPublished - 2014
Externally publishedYes

Fingerprint

Output Feedback Control
Switched Systems
Feedback control
Nonlinear systems
Stability Analysis
Nonlinear Systems
Tangent function
Nonlinearity
Hyperbolic tangent
Neural networks
Switched Linear Systems
Activation Function
Recurrent Neural Networks
Output Feedback
Asymptotic stability
Linear matrix inequalities
Stability Condition
Asymptotic Stability
Artificial Neural Network
Linear systems

Cite this

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title = "Stability analysis and output feedback control for a class of switched nonlinear systems",
abstract = "The problem of stability analysis and output feedback control for a class of switched nonlinear systems is addressed in this paper. The subsystems are from the class of so-called Φ-systems (σ-systems). The standard saturation and the hyperbolic tangent (popular activation function in neural networks) are examples of this type of nonlinearity. The discrete-time recurrent artificial neural network is a special case of Φ-systems. Furthermore, results related to this class of nonlinear systems have potential applications in the classical problems related to uncertain nonlinearities such as Lure systems. Two linear matrix inequality-based (LMI) sufficient conditions for asymptotic stability are proposed for these switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. Two conditions for output feedback controller synthesis based on the proposed stability conditions are presented. The results are further illustrated by numerical examples.",
author = "Shaker, {Hamid Reza}",
year = "2014",
doi = "10.1504/IJMIC.2014.066264",
language = "English",
volume = "22",
journal = "International Journal of Modelling, Identification and Control",
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publisher = "Inderscience Publishers",
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}

Stability analysis and output feedback control for a class of switched nonlinear systems. / Shaker, Hamid Reza.

In: International Journal of Modelling, Identification and Control, Vol. 22, No. 4, 2014.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Stability analysis and output feedback control for a class of switched nonlinear systems

AU - Shaker, Hamid Reza

PY - 2014

Y1 - 2014

N2 - The problem of stability analysis and output feedback control for a class of switched nonlinear systems is addressed in this paper. The subsystems are from the class of so-called Φ-systems (σ-systems). The standard saturation and the hyperbolic tangent (popular activation function in neural networks) are examples of this type of nonlinearity. The discrete-time recurrent artificial neural network is a special case of Φ-systems. Furthermore, results related to this class of nonlinear systems have potential applications in the classical problems related to uncertain nonlinearities such as Lure systems. Two linear matrix inequality-based (LMI) sufficient conditions for asymptotic stability are proposed for these switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. Two conditions for output feedback controller synthesis based on the proposed stability conditions are presented. The results are further illustrated by numerical examples.

AB - The problem of stability analysis and output feedback control for a class of switched nonlinear systems is addressed in this paper. The subsystems are from the class of so-called Φ-systems (σ-systems). The standard saturation and the hyperbolic tangent (popular activation function in neural networks) are examples of this type of nonlinearity. The discrete-time recurrent artificial neural network is a special case of Φ-systems. Furthermore, results related to this class of nonlinear systems have potential applications in the classical problems related to uncertain nonlinearities such as Lure systems. Two linear matrix inequality-based (LMI) sufficient conditions for asymptotic stability are proposed for these switched nonlinear systems. These conditions are analogous counterparts for switched linear systems which are shown to be easily verifiable and suitable for design problems. Two conditions for output feedback controller synthesis based on the proposed stability conditions are presented. The results are further illustrated by numerical examples.

U2 - 10.1504/IJMIC.2014.066264

DO - 10.1504/IJMIC.2014.066264

M3 - Journal article

VL - 22

JO - International Journal of Modelling, Identification and Control

JF - International Journal of Modelling, Identification and Control

SN - 1746-6172

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ER -