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H∞ Control Problem of Discrete 2-D Switched Mixed Delayed Systems Using the Improved Lyapunov-Krasovskii Functional

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Abstract

This paper deals with the problem of exponential stability and H∞ control of two-dimensional (2-D) switched discrete systems with mixed time-varying delays. Firstly, this work suggests some improvements to Lyapunov-Krasovskii functional (LKF) discussed in the previous literature. Such improvements have been achieved by introducing some new terms containing the summations of state vector in single and double forms in an effort to capture the extra information related to time delays. Secondly, delay-dependent conditions based on the improved LKF are derived for the exponential stability and H∞ performance of 2-D switched systems in the form of linear matrix inequalities (LMIs) by virtue of the average dwell time approach. Thirdly, a state-feedback controller is designed to ensure the exponential stability of the overall closed-loop system under consideration with a desirable H∞ disturbance attenuation level γ. Finally, a suitable example is provided which highlights the benefits of the proposed results by comparing them with the results available in literature both in terms of conservativeness and computational burden.

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Author information

Authors and Affiliations

  1. College of Energy and Electrical Engineering, Hohai University, Nanjing, 210098, People’s Republic of China

    Zhaoxia Duan

  2. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Lahore Campus, Lahore, 54000, Pakistan

    Imran Ghous & Jahanzeb Akhtar

  3. School of Automation, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Yuanqing Xia

Authors
  1. Zhaoxia Duan
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  2. Imran Ghous
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  3. Yuanqing Xia
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  4. Jahanzeb Akhtar
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Correspondence to Imran Ghous.

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Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Yoshito Ohta. This work was supported by National Natural Science Foundation of China under Grant No. 61703137 and the Fundamentals Research Funds for the Central Universities under Grant No. 2019B14814.

Zhaoxia Duan was born in Sichuan Province, China, in 1989. She received her B.S. degree in Automation and a Ph.D. degree in Control Theory and Control Engineering from Nanjing University of Science and Technology(NUST), Nanjing, China, in 2011 and 2017, respectively. Now she is a lecturer in the College of Energy and Electrical Engineering from Hohai University, Nanjing China. Her areas of interest include robust control and filtering, two-dimensional systems, positive systems, switched systems and nonlinear systems.

Imran Ghous received his B.Sc. and M.Sc. degrees in Electrical Engineering from University of Engineering and Technology, Taxila, Pakistan, in 2011 and 2013, respectively. He completed his Ph.D. degree in Control Science and Engineering from Nanjing University of Science and Technology, P. R. China in 2016. He is currently serving as an Assistant Professor at the Department of Electrical Engineering, COMSATS University Islamabad (Lahore Campus), Pakistan. He received his M.Sc. Full-Time Scholarship from the University of Engineering and Technology, Taxila, Pakistan during his Master’s degree. His Ph.D. degree was jointly funded by Nanjing Government-Nanjing University of Science and Technology Joint Scholarship Class-A and UNESCO/Peoples’ Republic of China (The Great Wall) Co-Sponsored Fellowships Programme (2015-2016). Based upon his academic and research performance he also received cash prize under the Elite International Student Scholarship Programme through China Scholarship Council (CSC). He is a very active reviewer of many international journals. His research interests mainly include 2-D systems, switched systems, non-linear systems, and positive systems, etc.

Yuanqing Xia was born in Anhui, China, in 1971, and graduated from the Department of Mathematics, Chuzhou University, Chuzhou, China, in 1991. He received his M.Sc. degree in Fundamental Mathematics from Anhui University, China, in 1998, and his Ph.D. degree in Control Theory and Control Engineering from Beijing University of Aeronautics and Astronautics, Beijing, China, in 2001. He is currently a full professor and the Dean of School of Automation, Beijing Institute of Technology, Beijing. He is the recepient of many national and international awards. His current research interests are in the fields of networked control systems, robust control and signal processing, active disturbance rejection control and flight control. He has authored and co-authored more than 100 internal journal articles and published eight monographs as well. He has also served as an editor and associate editor of well reputed international journals.

Jahanzeb Akhtar completed his undergraduate degree in Electrical Engineering with control specialisation from City University London in 2010. Shortly thereafter, he joined the centre for sensors and instrumentation at Brunel University London for the degree of doctor of philosophy in Electrical Engineering (advance control systems) where he closely worked with the European organisation for nuclear research (CERN) and Muon Ionisation Cooling Experiment (MICE) communities on the instrumentation and measurement systems (particle detectors) for efficient track re-construction, improvements in relative observability and computational complexity. He was awarded with a Ph.D. degree for his research on efficient particle tracking in high energy physics experiments in 2015. He moved to the department of Electrical Engineering at Comsats as an assistant professor in July 2016. His research interests mainly include control theory applications, state estimation (bad data and outlier detection and trearment), non-linear tracking in general and track reconstruction algorithm development and computing in particular for high energy physics experiments such as MICE at Rutherford Appleton laboratory Oxford and Large Hadron Collider (LHC) at CERN.

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Duan, Z., Ghous, I., Xia, Y. et al. H∞ Control Problem of Discrete 2-D Switched Mixed Delayed Systems Using the Improved Lyapunov-Krasovskii Functional. Int. J. Control Autom. Syst. 18, 2075–2087 (2020). https://doi.org/10.1007/s12555-019-0331-y

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