© The Institution of Engineering and Technology
This study proposes a new summation inequality, called the free-matrix-based summation inequality, which further extends certain existing summation inequalities in the literature. Less conservative stability criteria are proposed for discrete-time systems with time-varying delays. Numerical examples are provided to demonstrate the improvement of the proposed approach.
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17. Seuret, A., Gouaisbaut, F.: ‘Wirtinger-based integral inequality: application to time-delay systems’, Automatica, 2013, 49, (9), pp. 2860–2866 (doi: 10.1016/j.automatica.2013.05.030).
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12. Zhang, B., Xu, S., Zou, Y.: ‘Improved stability criterion and its applications in delayed controller design for discrete-time systems’, Automatica, 2008, 44, (11), pp. 2963–2967 (doi: 10.1016/j.automatica.2008.04.017).
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9. Wu, L., Su, X., Shi, P., et al.: ‘A new approach to stability analysis and stabilization of discrete-time TS fuzzy time-varying delay systems’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2011, 41, (1), pp. 273–286 (doi: 10.1109/TSMCB.2010.2051541).
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10. Kwon, O.-M., Park, M.-J., Park, J.-H., et al.: ‘Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov–Krasovskii functional’, J. Franklin Inst., 2013, 350, (3), pp. 521–540 (doi: 10.1016/j.jfranklin.2012.12.013).
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5. Peng, C.: ‘Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality’, IET Control Theory Appl., 2012, 6, (3), pp. 448–453 (doi: 10.1049/iet-cta.2011.0109).
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18. Zeng, , H., , He, , Y., , Wu, , M., , et al: ‘Free-matrix-based integral inequality for stability analysis of systems with time-varying delay’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 2768–2772.
-
25)
-
15. Liu, J., Zhang, J.: ‘Note on stability of discrete-time time-varying delay systems’, IET Control Theory Appl., 2012, 6, (2), pp. 335–339.
-
26)
-
13. Yue, D., Tian, E., Zhang, Y.: ‘A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay’, Int. J. Robust Nonlinear Control, 2009, 19, (13), pp. 1493–1518.
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27)
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12. Zhang, B., Xu, S., Zou, Y.: ‘Improved stability criterion and its applications in delayed controller design for discrete-time systems’, Automatica, 2008, 44, (11), pp. 2963–2967.
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30)
-
2. Fridman, E., Shaked, U.: ‘Stability and guaranteed cost control of uncertain discrete delay systems’, Int. J. Control, 2005, 78, (4), pp. 235–246.
-
31)
-
22. Li, X., Gao, H.: ‘A new model transformation of discrete-time systems with time-varying delay and its application to stability analysis’, IEEE Trans. Autom. Control, 2011, 56, (9), pp. 2172–2178.
-
32)
-
23. Gonzalez, A., Guerra, T.-M.: ‘An improved robust stabilization method for discrete-time fuzzy systems with time-varying delays’, J. Franklin Inst., 2014, 351, (11), pp. 5148–5161.
-
33)
-
24. Park, P.-G., Ko, J.-W., Jeong, C.: ‘Reciprocally convex approach to stability of systems with time-varying delays’, Automatica, 2011, 47, (1), pp. 235–238.
-
34)
-
3. Kao, C.-Y.: ‘On stability of discrete-time LTI systems with varying time delays’, IEEE Trans. Autom. Control, 2012, 57, (5), pp. 1243–1248.
-
35)
-
21. Huang, H., Feng, G.: ‘Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay’, IET Control Theory Appl., 2010, 4, (10), pp. 2152–2159.
-
36)
-
7. He, Y., Wu, M., Liu, G.P., et al.: ‘Output feedback stabilization for a discrete-time system with a time-varying delay’, IEEE Trans. Autom. Control, 2008, 53, (10), pp. 2372–2377.
-
37)
-
8. Gao, H., Chen, T.: ‘New results on stability of discrete-time systems with time-varying state delay’, IEEE Trans. Autom. Control, 2007, 52, (2), pp. 328–334.
-
38)
-
17. Seuret, , A., , Gouaisbaut, , F., , Fridman, , E.: ‘Stability of discrete-time systems with time-varying delays via a novel summation inequality’, IEEE Trans. Autom. Control, 2015, 60, (10), pp. 2740–2745.
-
39)
-
11. Shao, H., Han, Q.-L.: ‘New stability criteria for linear discrete-time systems with interval-like time-varying delays’, IEEE Trans. Autom. Control, 2011, 56, (3), pp. 619–625.
-
40)
-
14. Meng, X., Lam, J., Du, B., et al.: ‘A delay-partitioning approach to the stability analysis of discrete-time systems’, Automatica, 2010, 46, (3), pp. 610–614.
-
41)
-
5. Peng, C.: ‘Improved delay-dependent stabilisation criteria for discrete systems with a new finite sum inequality’, IET Control Theory Appl., 2012, 6, (3), pp. 448–453.
-
42)
-
6. Zhang, X.-M., Han, Q.-L.: ‘Delay-dependent robust H∞ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality’, IEEE Trans. Circuits Syst. II, Exp. Briefs, 2006, 53, (12), pp. 1466–1470.
-
43)
-
20. Xu, S., Lam, J., Zhang, B.: ‘A new result on the delay-dependent stability of discrete systems with time-varying delays’, Int. J. Robust Nonlinear Control, 2014, 24, (16), pp. 2512–2521.
-
44)
-
4. Kim, S.-H.: ‘Relaxed inequality approach to robust H∞ stability analysis of discrete-time systems with time-varying delay’, IET Control Theory Appl., 2012, 6, (13), pp. 2149–2156.
-
45)
-
16. Seuret, A., Gouaisbaut, F.: ‘Wirtinger-based integral inequality: application to time-delay systems’, Automatica, 2013, 49, (9), pp. 2860–2866.
-
46)
-
10. Kwon, O.-M., Park, M.-J., Park, J.-H., et al.: ‘Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov–Krasovskii functional’, J. Franklin Inst., 2013, 350, (3), pp. 521–540.
-
47)
-
9. Wu, L., Su, X., Shi, P., et al.: ‘A new approach to stability analysis and stabilization of discrete-time TS fuzzy time-varying delay systems’, IEEE Trans. Syst. Man Cybern. B, Cybern., 2011, 41, (1), pp. 273–286.
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