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Finite-time stability for a linear discrete-time delay systems by using discrete convolution: An LMI approach

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Abstract

The problem of finite-time stability for a class of linear discrete-time systems with state delay is studied. The Lyapunov-Krasovskii-like functional which is based on discrete convolutions of delayed state vector and time-dependent discrete vector functions is used. In order to obtain much less conservative results, new sufficient condition is derived in form of linear matrix inequalities. Numerical example is given to demonstrate the effectiveness of the proposed stability criterion. It was shown that the obtained results are less conservative than some existing ones in the literature. A computer simulation was performed for the analysis of the dynamical behaviour of this system.

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Author information

Authors and Affiliations

  1. Faculty of Technology, Department of Engineering Sciences and Applied Mathematics, University of Nis, Bulevar oslobodjenja 124, 16000, Leskovac, Serbia

    Sreten B. Stojanovic

  2. Faculty of Mechanical Engineering, Department of Control Engineering, University of Belgrade, Belgrade, Kraljive Marije 16, Serbia

    Dragutin Lj. Debeljkovic

  3. Faculty of Technical Science, University of Pristina, Kosovska Mitrovica, Serbia

    Milan A. Misic

Authors
  1. Sreten B. Stojanovic
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  2. Dragutin Lj. Debeljkovic
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  3. Milan A. Misic
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Corresponding author

Correspondence to Sreten B. Stojanovic.

Additional information

Recommended by Associate Editor Do Wan Kim under the direction of Editor PooGyeon Park. This paper is part of the project ON147001 at the Mathematical Institute SANU Belgrade and University of Nis, Faculty of Technology, and was supported by Ministry of Education, Science and Technological Development of the Republic of Serbia.

Sreten B. Stojanovic received his M.S. degree in Electrical Engineering and his Ph.D. degree in Control Engineering from the Belgrade University, Serbia, in 1995 and 2006, respectively. Now he is an associate professor of University of Nis. His research interests include time-delay systems, singular systems, stability and robust control.

Dragutin Lj. Debeljkovic received all degrees from the University of Belgrade a B.S. in Thermo-energetic Engineering, (1974) an M. Sc. (1977) and Ph.D., (1979) both in Control and System Science Engineering. He is currently a full professor of University of Belgrade, Faculty of Mechanical Engineering. His research interests include modelling, time-delay systems, singular systems and stability. Since 2004. Prof. Debeljkovic is a Europe regional and associate editor of International Journal of Information and System Science. Milan A. Misic received his M.S. and Ph.D. degrees in Mechanical Engineering from the University of Kragujevac, Serbia, in 1997 and 2006, respectively. He is currently an assistant professor of University of Kosovka Mitrovica. His research interests include automation of production system

Milan A. Misic received his M.S. and Ph.D. degrees in Mechanical Engineering from the University of Kragujevac, Serbia, in 1997 and 2006, respectively. He is currently an assistant professor of University of Kosovka Mitrovica. His research interests include automation of production system.

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Stojanovic, S.B., Debeljkovic, D.L. & Misic, M.A. Finite-time stability for a linear discrete-time delay systems by using discrete convolution: An LMI approach. Int. J. Control Autom. Syst. 14, 1144–1151 (2016). https://doi.org/10.1007/s12555-014-0447-z

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  • DOI: https://doi.org/10.1007/s12555-014-0447-z

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