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Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay

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  • Control Theory and Applications
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Abstract

This article presents some novel results on sampled-data H∞ control for a class of linear systems. The proposed system is affected by time-varying delay and external disturbance. The main goal of this paper is to transform the original system into an equivalent two interconnected subsystems through the combination of input-output approach and scaled small gain (SSG) theorem. Then, the three term approximation method is adopted to approximate the time-varying delay. By incorporating Lyapunov-Krasovskii functional and wirtinger integral inequality, a new set of sufficient conditions is obtained in terms of linear matrix inequalities (LMIs), which guarantee the stability of the closed loop system, and a H∞ norm bound performances. Finally, the applicability of the developed control design technique and its less conservativeness over other existing ones are proven by means of simulation examples.

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Authors and Affiliations

  1. Department of Physics, Faculty of Sciences Dhar El Mehraz, University Sidi Mohammed Ben Abdellah, LESSI, BP 1796, Fes-Atlas, Morocco

    Ouarda Lamrabet, El Houssaine Tissir, Nabil El Fezazi & Fatima El Haoussi

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  1. Ouarda Lamrabet
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  2. El Houssaine Tissir
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  3. Nabil El Fezazi
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  4. Fatima El Haoussi
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Correspondence to Ouarda Lamrabet.

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Recommended by Associate Editor Yonghao Gui under the direction of Editor PooGyeon Park.

Ouarda Lamrabet received her Master’s degree in signals systems and computer science from the University Sidi Mohammed Ben Abdellah, Faculty of Sciences, Morocco in 2015. She is currently a Ph.D. student in the same faculty. Her main research interests are robust and H∞ control, sampled-data control, systems with saturating actuators.

El Houssaine Tissir received his Diploma of higher studies and Doctorate of state degree from the University Sidi Mohammed Ben Abellah, Faculty of Sciences, Morocco in 1992 and 1997, respectively. He is now a Professor at the University Sidi Mohammed Ben Abdellah. His research interests include robust and H∞ control, singular systems, switched systems, time delay systems, systems with saturating actuators and TCP/IP networks.

Nabil El Fezazi received his Master’s and his Ph.D. degrees from the University Sidi Mohammed Ben Abdellah, Faculty of Sciences, Morocco, in 2013 and 2018, respectively. His main research interests are robust and H∞ control, sampled-data control, steer by wire systems, TCP/IP networks.

Fatima El Haoussi received her Ph.D. degree from the University Sidi Mohammed Ben Abdellah, Faculty of Sciences, Morocco in 2008. She was a Professor at the Polydisciplinary Faculty of Nador, Morocco from 2012 to 2018. She is now a Professor at the Faculty of Sciences Fez. Her research interests include robust and H∞ control, sampled-data control, teleoperation systems, systems with saturating actuators, time delay systems, TCP/IP networks, wind tunnel.

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Lamrabet, O., Tissir, E.H., El Fezazi, N. et al. Input-output Approach and Scaled Small Gain Theorem Analysis to Sampled-data Systems with Time-varying Delay. Int. J. Control Autom. Syst. 18, 2242–2250 (2020). https://doi.org/10.1007/s12555-019-0173-5

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  • DOI: https://doi.org/10.1007/s12555-019-0173-5

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