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This study investigates the input-to-state stability issue and the Lyapunov–Krasovskii functional construction for a class of switched non-linear systems with time-varying input delay under mode-dependent average dwell-time scheme. The authors assume that an exponential stabilising state feedback controller has been predesigned for the nominal system and the Lyapunov function for the nominal closed-loop system is available. When input delay and disturbance are involved, the closed-loop system may be unstable under the average dwell time for the nominal system. In allusion to this instance, by introducing a positive definite relaxation matrix and constructing a novel piecewise Lyapunov–Krasovskii functional based on the known Lyapunov function, they provide sufficient conditions and the upper bound of the input delay such that the closed-loop system is input-to-state stable with respect to the disturbance. Finally, numerical examples are given to illustrate the effective of the proposed method.
References
-
-
1)
-
37. Sun, X., Wang, W.: ‘Input-to-sate stability for hybrid delayed systems with unstable continuous dynamics’, Automatica, 48, (9), 2012, pp. 2359–2364 (doi: 10.1016/j.automatica.2012.06.056).
-
2)
-
M. Sun ,
J. Zhao ,
D.J. Hill
.
Stability and ℒ2 gain for switched delay systems: a delay-dependent method.
Automatica
,
10 ,
1769 -
1774
-
3)
-
13. Xiang, Z.R., Liang, C.Y., Chen, Q.W.: ‘Robust L2 − L∞ filtering for switched systems under asynchronous switching’, Commun. Nonlinear Sci. Numer. Simul., 2011, 16, (8), pp. 3303–3318 (doi: 10.1016/j.cnsns.2010.10.029).
-
4)
-
12. Li, Q.K., Zhao, J., Liu, X.J., Dimirovski, G.M.: ‘Observer-based tracking control for switched linear systems with time-varying delay’, Int. J. Robust Nonlinear Control, 2011, 21, (3), pp. 309–327 (doi: 10.1002/rnc.1597).
-
5)
-
E. Fridman ,
A. Seuret ,
J. Richard
.
Robust sampled-data stabilization of linear systems: an input delay approach.
Automatica
,
8 ,
1441 -
1446
-
6)
-
X. Zhao ,
L. Zhang ,
P. Shi ,
M. Liu
.
Stability and stabilization of switched linear systems with mode-dependent average dwell time.
IEEE Trans. Autom. Control
-
7)
-
H. Lin ,
P.J. Anstaklis
.
Stability and stabilisability of switched linear systems: a survey of recent results.
IEEE Trans. Autom. Control
,
308 -
322
-
8)
-
1. Malisoff, M., Mazenc, F., Zhang, F.M.: ‘Stability and robustness analysis for curve tracking control using input-to-state stability’, IEEE Trans. Autom. Control, 2012, 57, (5), pp. 1320–1326 (doi: 10.1109/TAC.2011.2174664).
-
9)
-
F. Mazenc ,
P-A. Bliman
.
Backstepping design for time-delay nonlinear systems.
IEEE Trans. Autom. Control
,
1 ,
149 -
154
-
10)
-
11. Wu, L., Zheng, W.X.: ‘ℋ∞ model reduction for switched hybrid systems with time-varying delay’, Automatica, 2009, 45, (1), pp. 186–193 (doi: 10.1016/j.automatica.2008.06.024).
-
11)
-
F. Mazenc ,
M. Malisoff ,
Z.L. Lin
.
Further results on input-to-state stability for nonlinear systems with delayed feedbacks.
Automatica
,
9 ,
2415 -
2421
-
12)
-
J. Zhao ,
D.J. Hill
.
On stability, L2 gain and H∞ control for switched systems.
Automatica
,
5 ,
1220 -
1232
-
13)
-
5. Sun, X.M., Liu, G.P., Wang, W., Rees, D.: ‘L2-gain of systems with input delays and controller temporary failure: zero-order hold model’, IEEE Trans. Control Syst. Technol., 2011, 19, (3), pp. 699–706 (doi: 10.1109/TCST.2010.2050320).
-
14)
-
Z. Wang ,
D.W.C. Ho ,
Y. Liu ,
X. Liu
.
Robust H-infinity control for a class of nonlinear discrete time-delay stochastic systems with missing measurements.
Automatica
,
3 ,
684 -
691
-
15)
-
18. Lian, J., Shi, P., Feng, Z.: ‘Passivity and passification for a class of uncertain switched stochastic time-delay systems’, IEEE Trans. Cybern., 2013, 43, (1), pp. 3–13 (doi: 10.1109/TSMCB.2012.2198811).
-
16)
-
22. Ito, H., Jiang, Z.P., Pepe, P.: ‘Construction of Lyapunov–Krasovskii functionals for networks of iISS retarded systems in small-gain formulation’, Automatica, 2013, 49, (11), pp. 3246–3257 (doi: 10.1016/j.automatica.2013.08.020).
-
17)
-
19. Liu, J., Liu, X.Z., Xie, W.C.: ‘Input-to-state stability of impulsive and switching hybrid systems with time-delay’, Automatica, 2011, 47, pp. 899–908 (doi: 10.1016/j.automatica.2011.01.061).
-
18)
-
19. Wang, Y.E., Sun, X.M., Shi, P., Zhao, J.: ‘Input-to-state stability of switched nonlinear systems with time delays under asynchronous switching’, IEEE Trans. Cybern., 2013, 43, (6), pp. 2261–2265 (doi: 10.1109/TCYB.2013.2240679).
-
19)
-
9. Sun, Z.D.: ‘Robust switching of discrete-time switched linear systems’, Automatica, 2012, 48, (1), pp. 239–242 (doi: 10.1016/j.automatica.2011.10.004).
-
20)
-
21. Wang, Y.E., Sun, X.M., Wang, Z., Zhao, J.: ‘Construction of Lyapunov–Krasovskii functionals for switched nonlinear systems with input delay’, Automatica, 2014, 50, (4), pp. 1249–1253 (doi: 10.1016/j.automatica.2014.02.029).
-
21)
-
9. Chen, W.-H., Zheng, W.X.: ‘Exponential stability of nonlinear time-delay systems with delayed impulse effects’, Automatica, 2011, 47, (5), pp. 1075–1083 (doi: 10.1016/j.automatica.2011.02.031).
-
22)
-
7. Liberzon, D.: ‘Switching in systems and control’ (Berlin: Birkhauser, 2003).
-
23)
-
14. Haimovich, H., Seron, M.M.: ‘Bounds and invariant sets for a class of switching systems with delayed-state-dependent perturbations’, Automatica, 2013, 49, (3), pp. 748–754 (doi: 10.1016/j.automatica.2012.10.002).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2014.0526
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