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Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

Author

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  • K. Ramakrishnan

    (Indian Institute of Technology Kharagpur)

  • G. Ray

    (Indian Institute of Technology Kharagpur)

Abstract

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

Suggested Citation

  • K. Ramakrishnan & G. Ray, 2011. "Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay," Journal of Optimization Theory and Applications, Springer, vol. 149(2), pages 366-384, May.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:2:d:10.1007_s10957-010-9784-0
    DOI: 10.1007/s10957-010-9784-0
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    References listed on IDEAS

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    1. P. T. Nam & V. N. Phat, 2009. "Robust Stabilization of Linear Systems with Delayed State and Control," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 287-299, February.
    2. Liu, Xin-Ge & Wu, Min & Martin, Ralph & Tang, Mei-Lan, 2007. "Delay-dependent stability analysis for uncertain neutral systems with time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(1), pages 15-27.
    3. M. S. Mahmoud & P. Shi & A. W. A. Saif, 2009. "Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 583-601, September.
    4. Yu, Ker-Wei & Lien, Chang-Hua, 2008. "Stability criteria for uncertain neutral systems with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 650-657.
    5. M. S. Mahmoud & Y. Xia, 2009. "Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 329-355, November.
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