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Robust Stability Analysis of Time-varying Delay Systems via an Augmented States Approach

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  • Control Theory and Applications
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Abstract

This paper focuses on the robust stability analysis of linear systems with time varying delays. The second derivative of the state is used to construct a novel Lyapunov-Krasovskii functional (LKF). Then, both the integrals and derivatives of the states along with the delayed states could be taken into consideration in handling of the LKF. We introduce these augmented variables and establish correlations between them. Moreover, our approach makes it available that quadratic convex combination can be applied not only to the time delay, but also to the derivative of it. Robust stability criteria are presented, and numerical examples illustrate that the methods are less conservative.

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Author information

Authors and Affiliations

  1. School of Aeronautic Science and Engineering, Beihang University, Haidian District, Beijing, China

    Chao-Yang Dong, Ming-Yu Ma & Si-Qian Ma

  2. School of Automation Science and Electrical Engineering, Beihang University, Haidian District, Beijing, China

    Qing Wang

Authors
  1. Chao-Yang Dong
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  2. Ming-Yu Ma
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  3. Qing Wang
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  4. Si-Qian Ma
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Corresponding author

Correspondence to Ming-Yu Ma.

Additional information

Recommended by Associate Editor Ohmin Kwon under the direction of Editor PooGyeon Park. This work is supported by the National Natural Science Foundation of China (Grant No. 61374012).

Chao-Yang Dong received his Ph.D. degree in Guidance, Navigation and Control from Beihang University. He is currently a professor of at the School of Aeronautic Science and Engineering, Beihang University. His research interests inlcude modeling and control of flight vehicles, networked control systems, and synthesis of aerospace electrical system.

Ming-Yu Ma is currently working toward a Ph.D. degree at the School of Aeronautic Science and Engineering, Beihang University. His research interests include time delay systems, multi-agent systems, and flight control systems.

Qing Wang received her Ph.D. degree in Guidance, Navigation and Control from Northwestern Polytechnical University in 1996. She is currently a professor at the School of Automation Science and Electrical Engineering, Beihang University. Her research interests include switching systems, time delay systems, and fault-tolerant control.

Si-Qian Ma is currently working on the M.E. degree in the School of Aeronautic Science and Engineering, Beijing University. His research interests include modeling of flight vehicles, formation control and simulation.

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Dong, CY., Ma, MY., Wang, Q. et al. Robust Stability Analysis of Time-varying Delay Systems via an Augmented States Approach. Int. J. Control Autom. Syst. 16, 1541–1549 (2018). https://doi.org/10.1007/s12555-017-0398-2

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