AUTHORS: Huimin Wang, Yali Dong, Mengxiao Deng
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ABSTRACT: In this paper, the problems of H∞ finite-time boundedness for a class of discrete-time systems with time-varying delay and norm-bounded disturbance is investigated. By constructing a time-varying Lyapunov-Krasovskii functional and utilizing the linear matrix inequality approach, the H∞ finite-time boundedness criterion is established to ensure that the discrete-time system with time-varying delay and norm-bounded disturbance is H∞ finite-time bounded. A numerical example is provided to demonstrate the effectiveness of the theoretical results.
KEYWORDS: - H∞ finite-time boundedness; Discrete-time systems; Time-varying delay; Lyapunov-Krasovskii functional
REFERENCES:
[1] Y. Dong, L. Chen, S. Mei, Stability analysis and observer design for discrete-time systems with interval time- varying delay, Optim. Control Appl. Methods, Vol. 7, 2016, pp. 340-358.
[2] G. Wang, J. Cao, J. Liang, Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters, Nonlinear Dyn. Vol. 57, 2009. pp. 209-218.
[3] S. Lakshmanan, T. Senthilkumar, P. Balasubramaniam, Improved results on robust stability of neutral systems with mixed time-varying delays and nonlinear perturbations, Appl. Math. Model, Vol. 35, No. 11. 2011, pp. 5355-5368.
[4] F. Amato, R. Ambrosino, M. Ariola, G. De Tommasi, Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties, Internat. J. Robust Nonlinear Control, Vol. 21, No. 10. 2011, 1080-1092.
[5] E. Moulay, M. Dambrine, N. Yeganefar, W. Perruquetti, Finite-time stability and stabilization of time-delay systems. Systems & Control Letters, Vol. 57, 2008, pp. 561-566.
[6] E. Moulay, W. Perruquetti, Finite time stability of differential inclusions. IMA Journal of Mathematical Control and Information, Vol. 22, 2005, pp. 465-475.
[7] L. Sun, G. Feng, Y. Wang, Finite-time stabilization and H∞ control for a class of nonlinear Hamiltonian descriptor systems with application to affine nonlinear descriptor systems. Automatica, Vol. 50, 2014, pp. 2090-2097.
[8] Y. Tian, Y. Cai, Y. Sun, H. Gao, Finite-time stability for impulsive switched delay systems with nonlinear disturbances, J. Franklin Inst. Vol. 353, No. 14, 2016, pp. 3578-3594.
[9] J. Zhang, Z. Han, W. Hai, Robust finite-time stability and stabilisation of switched positive systems, IET Control Theory Appl. Vol. 8, No. 1, 2014, pp. 67-75.
[10] G. Chen, Y. Yang, Finite-time stability of switched positive linear systems, Internat. J. Robust Nonlinear Control, Vol. 24, No. 1, 2014, pp. 179-190.
[11] R. Yang, Y. Wang, Finite-time stability and stabilization of a class of nonlinear time-delay systems. SIAM Journal on Control and Optimization, Vol. 50, 2012, pp. 3113-3131.
[12] R. Wu, Y. Lu, L. Chen, Finite-time stability of fractional delayed neural networks. Neurocomputing, Vol. 149, 2015, pp. 700-707.
[13] D. Efimov, A. Polyakov, E. Fridman, E. Perruquetti, J. P. Richard, Comments on finite-time stability of time-delay systems. Automatica, Vol. 50, 2014, pp. 1944-1947.
[14] G. Zong, R. Wang, W. Zheng, et al., Finite-time H∞ control for discrete-time switched nonlinear systems with time delay. International Journal of Robust & Nonlinear Control, Vol. 25, No. 6, 2015, pp. 914-936.
[15] S. B. Stojanovic, Robust finite-time stability of discrete time systems with interval time-varying delay and nonlinear perturbations. Journal of the Franklin Institute, Vol. 354 2017, pp. 4549-4572.
