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Stability criterion with less LMI variables for linear discrete-time systems with additive time-delays

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Abstract

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality (LMI) variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

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Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, West Bengal, 721 302, India

    K. Ramakrishnan & G. Ray

Authors
  1. K. Ramakrishnan
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  2. G. Ray
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Correspondence to K. Ramakrishnan.

Additional information

K. Ramakrishnan received the bachelor degree in electrical and electronics engineering from Government College of Technology, Coimbatore, Tamil Nadu, India in 1993 and master degree in control systems engineering from P.S.G. College of Technology, Coimbatore, Tamil Nadu, India in 1995. He is currently a full time QIP Research Scholar with the Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India. He is presently on a three year (2008–2011) deputation from Pondicherry Engineering College, Pondicherry, India for his Ph. D. programme in Indian Institute of Technology, Kharagpur through QIP scheme of AICTE, Government of India.

His research interests include LMI optimization and state space control theory.

G. Ray received the B.Tech. and M. Tech. degrees in electrical engineering and control systems from Jadvapur University, Kolkata, West Bengal, India, and Indian Institute of Technology, Kharagpur, West Bengal, India in 1974 and 1977, respectively. He received the Ph.D. degree in control engineering from Indian Institute of Technology, Delhi, India in 1982. From 1982–1984, he was working with National Institute of Technology, Jamshedpur, India. He joined as a faculty in the Department of Electrical Engineering, Indian Institute of Technology, Kharagpur in 1984 where he is a full professor now.

His research interests include robust control techniques, LMI optimization, time-delay systems, decentralized control, and large scale systems.

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Ramakrishnan, K., Ray, G. Stability criterion with less LMI variables for linear discrete-time systems with additive time-delays. Int. J. Autom. Comput. 8, 490–492 (2011). https://doi.org/10.1007/s11633-011-0608-y

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  • DOI: https://doi.org/10.1007/s11633-011-0608-y

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