Finite-time stability and finite-time weighted L2-gain analysis for switched systems with time-varying delay

IET Control Theory and Applications

Volumn 7, Issue 7, 2013, Pages 1058-1069

  Lin, Xiangze ^a,c   Du, Haibo ^b   Li, Shihua ^b   Zou, Yun ^c  

^a NANJING AGRICULTURAL UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

^c NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

AVERAGE DWELL TIME; DISTURBANCE TOLERANCE; FINITE TIME BOUNDEDNESS (FTB); FINITE TIME STABILITY; FIXED TIME INTERVAL; MULTIPLE LYAPUNOV-LIKE FUNCTIONS; SWITCHED LINEAR SYSTEM; TIME-VARYING DELAY;

LINEAR MATRIX INEQUALITIES; TIME VARYING CONTROL SYSTEMS;

SWITCHING SYSTEMS;

EID: 84886791327     PISSN: 17518644     EISSN: 17518652     Source Type: Journal    
DOI: 10.1049/iet-cta.2012.0551     Document Type: Article

References (65)

1. Liberzon, D., Morse, A.S.: 'Basic problems in stability and design of switched systems', IEEE Control Syst. Mag., 1999, 19, (5), pp. 59-70
2. Decarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson B.: 'Perspectives and results on the stability and stabilizability of hybrid systems', Proc. IEEE, 2000, 88, (7), pp. 1069-1082
3. Liberzon, D.: 'Switching in systems and control' (Boston, Brikhauser, 2003)
4. Sun, Z., Ge, S.: 'Switched linear systems: control and design' (Springer-Verlag, New York, 2004)
5. Zhai, G., Hu, B., Yasuda, K., Michel, A., 'Disturbance attenuation properties of time-controlled switched systems', J. Franklin Inst., 2001, 338, pp. 765-779
6. Branicky, M.S.: 'Multiple Lyapunov functions and other analysis tools for switched and hybrid systems', IEEE Trans. Autom. Control, 1998, 43, (4), pp. 475-482
7. Hespanha, J.P.: 'Uniform stability of switched linear systems: extensions of LaSalle's invariance principle', IEEE Trans. Autom. Control, 2004, 49, (4), pp. 470-482
8. Zhao, J., Hill, D.J.: 'Passivity and stability of switched systems: a multiple storage function method', Syst. Control Lett., 2008, 57, (2), pp. 158-164
9. Lin, H., Antsaklis, P.J.: 'Stability and stabilizability of switched linear systems: a survey on recent results', IEEE Trans. Autom. Control, 2009, 54, (2), pp. 308-322
10. Allerhand, L.I., Shaked, U.: 'Robust stability and stabilization of linear switched systems with dwell time', IEEE Trans. Autom. Control, 2011, 56, (2), pp. 381-386
11. Wu, L., Zheng, W.: 'Weighted H∞ model reduction for linear switched systems with time-varying delay', Automatica, 2009, 45, (1), pp. 186-193
12. Wu, L., Zheng, W., Gao, H.: 'Dissipativity-based sliding mode control of switched stochastic systems', IEEE Trans. Autom. Control, 2013, 58, (3), pp. 785-791
13. Ben Attia, S., Salhi, S., Ksouri, M.: 'Static switched output feedback stabilization for linear discrete-time switched systems', Int. J. Innov. Comput., Inf. Control, 2012, 8, (5(A)), pp. 3203-3213
14. Liu, Q., Wang, W., Wang, D.: 'New results on model reduction for discrete-time switched systems with time delay', Int. J. Innov. Comput. Inf. Control, 2012, 8, (5A), pp. 3431-3440
15. Michel, A.N., Hou, L.: 'Finite-time and practical stability of a class of stochastic dynamical systems'. Proc. 47th Conf. Decision and Control, Cancun, Mexico, December 2008, pp. 3452-3456
16. Mastellone, S., Abdallah, C. T., Dorato, P.: 'Stability and finite time stability of discrete-time nonlinear networked control systems'. Proc. American Control Conf., 2005, pp. 1239-1244
17. Pan, F., Chen, X., Lin, L.: 'Practical stability analysis of stochastic swarms'. Third Int. Conf. Innovative Computing Information and Control, 2008, pp. 32-36
18. Wang, L., Cai, L., Liu, X., Shen, X.: 'Pratical stability and bounds of heterogeneous AIMA/RED system with time delay'. IEEE Int. Conf. Communications, 2008, pp. 5558-5563
19. Dorato, P.: 'Short time stability in linear time-varying systems'. Proc. IRE Int. Convention Record Part 4, New York, 1961, pp. 83-87
20. Amato, F., Ariola, M., Dorato, P.: 'Finite-time control of linear systems subject to parametric uncertainties and disturbances', Automatica, 2001, 37, (9), pp. 1459-1463
21. Weiss, L., Infante, E.F.: 'Finite time stability under perturbing forces and on product spaces', IEEE Trans. Autom. Control, 1967, 12, (1), pp. 54-59
22. Kamenkov, G.: 'On stability of motion over a finite interval of time', J. Appl. Math. Mech., 1953, 17, (5), pp. 529-540 (in Russian)
23. Amato, F., Ariola, M.: 'Finite-time control of discrete-time linear system', IEEE Trans. Autom. Control, 2005, 50, (5), pp. 724-729
24. Amato, F., Ariola, M., Dorato, P.: 'Finite-time stabilization via dynamic output feedback', Automatica, 2006, 42, (2), pp. 337-342
25. Garcia, G., Tarbouriech, S., Bernussou, J.: 'Finite-time stabilization of linear time-varying continuous systems', IEEE Trans. Autom. Control, 2009, 54, (2), pp. 364-369
26. Liu, L., Sun, J.: 'Finite-time stabilization of linear systems via impulsive control', Int. J. Control, 2008, 81, (6), pp. 905-909
27. Zhao, S., Sun, J., Liu, L.: 'Finite-time stability of linear time-varying singular systems with impulsive effects', Int. J. Control, 2008, 81, (11), pp. 1824-1829
28. Amato, F., Ambrosino, R., Merola, A., Cosentino, C.: 'Finite-time stability of linear time-varying systems with jumps', Automatica, 2009, 45, (5), pp. 1354-1358
29. Amato, F., Ambrosino, R., Cosentino, C., De Tommasi, G.: 'Finitetime stabilization of impulsive dynamical linear systems', Nonlinear Anal., Hybrid Syst., 2011, 5, (1), pp. 89-101
30. Amato, F., Cosentino, C., Merola, A.: 'Sufficient conditions for finitetime stability and stabilization of nonlinear quadratic systems', IEEE Trans. Autom. Control, 2010, 55, (2), pp. 430-434
31. Amato, F., Merola, A., Cosentino, C.: 'Finite-time stability of linear time-varying systems: analysis and controller design', IEEE Trans. Autom. Control, 2010, 55, (4), pp. 1003-1008
32. Amato, F., Merola, A., Cosentino, C.: 'Finite-time control of discretetime linear systems: analysis and design conditions', Automatica 2010, 46, (5), pp. 919-924
33. Luan, X., Liu, F., Shi, P.: 'Robust finite-time H∞ control for nonlinear jump systems via neural networks', Circuits Syst. Signal Process., 2010, 29, (3), pp. 481-498
34. He, S., Liu, F.: 'Stochastic finite-time boundedness of Markovian jumping neural network with uncertain transition probabilities', Appl. Math. Model., 2011, 35, (6), pp. 2631-2638
35. Rosier, L.: 'Homogeneous Lyapunov function for homogeneous continuous vector field', Syst. Control Lett., 1992, 19, (4), pp. 467-473
36. Bhat, S.P., Bernstein, D.S.: 'Finite-time stability of continuous autonomous systems', SIAM J. Control Optim., 2000, 38, (3), pp. 751-766
37. Orlov, Y.: 'Finite time stability and robust control synthesis of uncertain switched systems', SIAM J. Control Optim., 2005, 43, (4), pp. 1253-1271
38. Hong, Y.G., Jiang, Z.P.: 'Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties', IEEE Trans. Autom. Control, 2006, 51, (12), pp. 1950-1956
39. Li, S., Du, H., Lin, X.: 'Finite-time consensus algorithm for multiagent systems with double-integrator dynamics', Automatica, 2011, 47, pp. 1706-1712
40. Meyer, C., Schroder, S., De Doncker, R.W.: 'Solid-state circuit breakers and current limiters for medium-voltage systems having distributed power systems', IEEE Trans. Power Electron., 2004, 19, (5), pp. 1333-1340
41. Buisson, J., Richard, P.Y., Cormerais, H.: 'On the stabilisation of switching electrical power converters', Proc. Hybrid Systems: Computation and Control, 2005, pp. 184-197
42. Lin, H., Zhai, G., Antsaklis, P.J.: 'Robust stability and disturbance attenuation analysis of a class of networked control systems'. Proc. IEEE Conf. Decision and Control, 2003, pp. 1182-1187
43. Sun, X., Liu, G., Wang, W., Rees, D.: 'Stability analysis for networked control systems based on average dwell time method', Int. J. Robust Nonlinear Control, 2010, 20, pp. 1774-1784
44. Xu, S., Lam, J.: 'A survey of linear matrix inequality techniques in stability analysis of delay systems', Int. J. Syst. Sci., 2009, 39, (12), pp. 1095-1113
45. Richard, J.P.: 'Time-delay systems: an overview of some recent advances and open problems', Automatica, 2003, 39, 1667-1694
46. Niculescu, S.I.: 'Delay effects on stability: a robust control approach' (Springer, Berlin, 2001)
47. Fridman, E., Shaked, U.: 'Delay-dependent stability and H∞ control: constant and time-varying delays', Int. J. Control, 2003, 76, 48-60
48. Gu, K., V. Kharitonov, L., Chen, J.: 'Stability of time-delay systems' (Birkhauser, Boston, 2003)
49. Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: 'Linear matrix inequalities in system and control theory', in Boyd, S. (Ed): 'SIAM studies in applied mathematics' (SIAM, Philadelphia, Pennsylvania, 1994)
50. Wu, M., He, Y., She, J., Liu, G.: 'Delay-dependent criteria for robust stability of time-varying delay systems', Automatica, 2004, 40, pp. 1435-1439
51. Sun, X., Zhao, J., Hill, D. J.: 'Stabilty and L2 gain analysis for switched delay systems: a delay-dependent method', Automatica, 2006, 42, (10), pp. 1769-1774
52. Sun, Y., Wang, L., Xie, G.: 'Delay-dependent robust stability and H∞ control for uncertain discrete-time switched systems with mode-dependent time delays', Appl. Math. Comput., 2007, 187, (2), pp. 1228-1237
53. Liu, X.: 'Stabilization of switched linear systems with mode-dependent time-varying delays', Appl. Math. Comput., 2010, 216, (9), pp. 2581-2586
54. Yan, P., O? zbay H: 'Stability analysis of switched time delay systems', SIAM J. Control Optim., 2008, 47, (2), pp. 936-949
55. Du, H., Lin, X., Li, S.: 'Finite-time boundedness and stabilization of switched linear systems', Kybernetika, 2010, 46, (5), pp. 970-889
56. Lin, X., Du, H., Li, S.: 'Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance', Appl. Math. Comput., 2011, 217, pp. 5982-5993
57. Hespanha, J.P., Morse, A.S.: 'Stability of switched systems with average dwell-time'. Proc. IEEE Conf. Decision and Control, 1999, pp. 2655-2660
58. Zhai, G.S., Hu, B., Yasuda, K., Michel, A.N.: 'Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach', Int. J. Syst. Sci., 2001, 32, (8), pp. 1055-1061
59. Sun, X. M., Liu, G. P., Rees, D., Wang, W.: 'Stability of systems with controller failure and time-varying delay', IEEE Trans. Autom. Control, 2008, 53, (10), pp. 2391-2396
60. Sun, X. M., Wang, W.: 'Input-to-sate stability for hybrid delayed systems with unstable continuous dynamics', Automatica, 2012, 48, (9), pp. 2359-2364
61. Sun, X. M., Wang, W., Liu, G. P., Zhao, J.: 'Stability analysis for linear switched systems with time-varying delay', IEEE Trans. Syst. Man Cybern. B, 2008, 38, (2), pp. 528-533
62. Gu, K.: 'A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time-delay systems', Int. J. Robust Nonlinear Control, 1999, 9, (1), pp. 1-14
63. Du, B. Z., Lam, J., Shu, Z.: 'A delay-partitioning projection approach to stability analysis of neutral systems'. Proc. 17th IFAC World Congress, Seoul, 2008, pp. 12348-12353
64. Su, X., Shi, P., Wu, L., Song, Y.: 'A novel approach to filter design for T-S fuzzy discrete-time systems with time-varying delay', IEEE Trans. Fuzzy Syst., 2012, 20, (6), pp. 1114-1129
65. Wu, L., Su, X., Shi, P., Qiu, J.: 'Model approximation for discretetime state-delay systems in the T-S fuzzy framework', IEEE Trans. Fuzzy Syst., 2011, 19, (2), pp. 366-378