Delay-dependent Stability Analysis for Uncertain Switched Neutral System
This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.
[1] S. Engell, S. Kowalewski, C. Schulz, O. Strusberg, Continuous-discrete
interactions in chemical processing plants, Proceedings of IEEE, Vol.
88, No. 7, pp. 1050-1068, 2000.
[2] R. Horowitz, P. Varaiya, Control design of an automated highway system.
Proceedings of IEEE, Vol. 88, No. 7, pp.913-925, 2000.
[3] C. Livadas, J. Lygeros, N.-A. Lynch, High-level modeling and analysis
of the traffic alert and collision avoidance system. Proceedings of IEEE,
Vol. 88, No. 7, pp.926-948, 2000.
[4] P. Varaiya, Smart cars on smart roads: Problems of control. IEEE
Transactions on Automatic Control, Vol. 38, No. 2, pp.195-207, 1993.
[5] D. Pepyne, C. Cassandaras, Optimal control of hybrid systems in manufacturing.
Proceedings of IEEE, Vol. 88, No. 7, pp.1008-1122, 2000.
[6] M. Song, T. Tran, N. Xi, Integration of task scheduling, action planning,
and control in robotic manufacturing systems. Proceedings of IEEE,
Vol. 88, No. 7, pp.1097-1107, 2000.
[7] P. Antsaklis, Special issue on hybrid systems: Theory and applications-
A brief introduction to the theory and applications of hybrid systems.
Proceedings of IEEE, Vol. 88, No. 7, pp.887-897, 2000.
[8] D. Liberzon, A.-S. Morse, Basic problems in stability and design of
switched systems. IEEE Control Systems Magazine, Vol. 19, No. 5,
pp.59-70, 1999.
[9] R. DeCarlo, M.-S. Branicky, S. Pettersson, B. Lennartson, Perspectives
and results on the stability and stabilizability of hybrid systems. Proceedings
of IEEE, Vol. 88, No. 7, pp.1069-1082, 2000.
[10] Z. Sun, S.-S. Ge, Analysis and synthesis of switched linear control
systems. Automatica, Vol 41, No. 2, pp.181-195, 2005.
[11] X.-M. Sun, J. Zhao, D.J. Hill, Stability and L2-gain analysis for
switched delay systems: A delay-dependent method. Automatica, Vol.
42, No. 10, pp.1769-1774, 2006.
[12] D. Liberzon, Switching in systems and control. Boston: Birkhauser,
2003.
[13] G.-S. Zhai, X.-P. Xu, H. Lin, A.-N. Michel, Analysis and design of
switched normal systems. Nonlinear Analysis: Theory, Methods &
Applications, Vol. 65, No. 12. pp.2248-2259, 2006.
[14] W.-H. Chen, W.-X. Zheng, Delay-dependent robust stabilization for
uncertain neutral systems with distributed delays. Automatica, Vol. 43,
No. 1, pp.95-104, 2007.
[15] Q.-L. Han, A descriptor system approach to robust stability of uncertain
neutral systems with discrete and distributed delays. Automatica, Vol.
40, No. 10, pp.1791-1796, 2004.
[16] J.-H. Park, Stability criterion for neutral differential systems with mixed
multiple time-varying delay arguments. Mathematics and Computers in
Simulation ,Vol. 59, No. 5, pp.401-412, 2002.
[17] H. Li, H.-B. Li, S.-M. Zhong, Some new simple stability criteria of
linear neutral systems with a single delay. Journal of Computational
and Applied Mathematics, Vol. 200, No.1, pp.441-447, 2007.
[18] L.-L. Xiong, S.-M. Zhong, J.-K. Tian, Novel robust stability criteria of
uncertain neutral systems with discrete and distributed delays. Chaos,
Solitons & Fractals, Vol. 40, No.2, pp.771-777, 2009.
[19] J.-W. Cao, S.-M. Zhong, Y.-Y. Hu, Global stability analysis for a class
of neural networks with varying delays and control input. Applied
Mathematics and Computation, Vol. 189, No. 2, pp.1480-1490, 2007.
[20] S.-Y. Xu, P. Shi, Y.-M. Chu, Y. Zou, Robust stochastic stabilization and
H∞ control of uncertain neutral stochastic time-delay systems. Journal
of Mathematical Analysis and Applications, Vol. 314, No. 1, pp.1-16,
2006.
[21] C. Bonnet, J.-R. Partington, Stabilization of some fractional delay
systems of neutral type. Automatica, Vol. 43, No. 12, pp. 2047 -2053,
2007.
[22] J.-H. Park, O. Kwon, On robust stabilization for neutral delay-differential
systems with parametric uncertainties and its application. Applied
Mathematics and Computation, Vol. 162, No. 3, pp.1167-1182, 2005.
[23] X.-M. Sun, J. Fu, H.-F. Sun, J. Zhao, Stability of linear switched
neutral delay systems. Proceedings of The Chinese Society for Electrical
Engineering, Vol. 25, No. 23, pp.42-46, 2005.
[24] Y.-P. Zhang, X.-Z. Liu, H. Zhu, Stability analysis and control synthesis
for a class of switched neutral systems. Applied Mathematics and
Computation, Vol. 190, No. 2, pp.1258-1266, 2007.
[25] D.-Y. Liu, X.-Z. Liu, S.-M. Zhong, Delay-dependent robust stability
and control synthesis for uncertain switched neutral systems with mixed
delays. Applied Mathematics and Computation, Vol. 202, No. 2, pp.828-
839, 2008.
[26] L. Xie, Output feedback H∞ control of systems with parameter uncertainty.
International Journal of Control, Vol. 63, No. 4, pp.741-750,
1996.
[27] S. Boyd , L.-E. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix
inequalities in systems and control theory. Philadelphia: SIAM, 1994.
[28] K. Gu, V.-L. Kharitonov, J. Chen, Stability of time-delay systems.
Birkhauser, Basel, 2003.
[1] S. Engell, S. Kowalewski, C. Schulz, O. Strusberg, Continuous-discrete
interactions in chemical processing plants, Proceedings of IEEE, Vol.
88, No. 7, pp. 1050-1068, 2000.
[2] R. Horowitz, P. Varaiya, Control design of an automated highway system.
Proceedings of IEEE, Vol. 88, No. 7, pp.913-925, 2000.
[3] C. Livadas, J. Lygeros, N.-A. Lynch, High-level modeling and analysis
of the traffic alert and collision avoidance system. Proceedings of IEEE,
Vol. 88, No. 7, pp.926-948, 2000.
[4] P. Varaiya, Smart cars on smart roads: Problems of control. IEEE
Transactions on Automatic Control, Vol. 38, No. 2, pp.195-207, 1993.
[5] D. Pepyne, C. Cassandaras, Optimal control of hybrid systems in manufacturing.
Proceedings of IEEE, Vol. 88, No. 7, pp.1008-1122, 2000.
[6] M. Song, T. Tran, N. Xi, Integration of task scheduling, action planning,
and control in robotic manufacturing systems. Proceedings of IEEE,
Vol. 88, No. 7, pp.1097-1107, 2000.
[7] P. Antsaklis, Special issue on hybrid systems: Theory and applications-
A brief introduction to the theory and applications of hybrid systems.
Proceedings of IEEE, Vol. 88, No. 7, pp.887-897, 2000.
[8] D. Liberzon, A.-S. Morse, Basic problems in stability and design of
switched systems. IEEE Control Systems Magazine, Vol. 19, No. 5,
pp.59-70, 1999.
[9] R. DeCarlo, M.-S. Branicky, S. Pettersson, B. Lennartson, Perspectives
and results on the stability and stabilizability of hybrid systems. Proceedings
of IEEE, Vol. 88, No. 7, pp.1069-1082, 2000.
[10] Z. Sun, S.-S. Ge, Analysis and synthesis of switched linear control
systems. Automatica, Vol 41, No. 2, pp.181-195, 2005.
[11] X.-M. Sun, J. Zhao, D.J. Hill, Stability and L2-gain analysis for
switched delay systems: A delay-dependent method. Automatica, Vol.
42, No. 10, pp.1769-1774, 2006.
[12] D. Liberzon, Switching in systems and control. Boston: Birkhauser,
2003.
[13] G.-S. Zhai, X.-P. Xu, H. Lin, A.-N. Michel, Analysis and design of
switched normal systems. Nonlinear Analysis: Theory, Methods &
Applications, Vol. 65, No. 12. pp.2248-2259, 2006.
[14] W.-H. Chen, W.-X. Zheng, Delay-dependent robust stabilization for
uncertain neutral systems with distributed delays. Automatica, Vol. 43,
No. 1, pp.95-104, 2007.
[15] Q.-L. Han, A descriptor system approach to robust stability of uncertain
neutral systems with discrete and distributed delays. Automatica, Vol.
40, No. 10, pp.1791-1796, 2004.
[16] J.-H. Park, Stability criterion for neutral differential systems with mixed
multiple time-varying delay arguments. Mathematics and Computers in
Simulation ,Vol. 59, No. 5, pp.401-412, 2002.
[17] H. Li, H.-B. Li, S.-M. Zhong, Some new simple stability criteria of
linear neutral systems with a single delay. Journal of Computational
and Applied Mathematics, Vol. 200, No.1, pp.441-447, 2007.
[18] L.-L. Xiong, S.-M. Zhong, J.-K. Tian, Novel robust stability criteria of
uncertain neutral systems with discrete and distributed delays. Chaos,
Solitons & Fractals, Vol. 40, No.2, pp.771-777, 2009.
[19] J.-W. Cao, S.-M. Zhong, Y.-Y. Hu, Global stability analysis for a class
of neural networks with varying delays and control input. Applied
Mathematics and Computation, Vol. 189, No. 2, pp.1480-1490, 2007.
[20] S.-Y. Xu, P. Shi, Y.-M. Chu, Y. Zou, Robust stochastic stabilization and
H∞ control of uncertain neutral stochastic time-delay systems. Journal
of Mathematical Analysis and Applications, Vol. 314, No. 1, pp.1-16,
2006.
[21] C. Bonnet, J.-R. Partington, Stabilization of some fractional delay
systems of neutral type. Automatica, Vol. 43, No. 12, pp. 2047 -2053,
2007.
[22] J.-H. Park, O. Kwon, On robust stabilization for neutral delay-differential
systems with parametric uncertainties and its application. Applied
Mathematics and Computation, Vol. 162, No. 3, pp.1167-1182, 2005.
[23] X.-M. Sun, J. Fu, H.-F. Sun, J. Zhao, Stability of linear switched
neutral delay systems. Proceedings of The Chinese Society for Electrical
Engineering, Vol. 25, No. 23, pp.42-46, 2005.
[24] Y.-P. Zhang, X.-Z. Liu, H. Zhu, Stability analysis and control synthesis
for a class of switched neutral systems. Applied Mathematics and
Computation, Vol. 190, No. 2, pp.1258-1266, 2007.
[25] D.-Y. Liu, X.-Z. Liu, S.-M. Zhong, Delay-dependent robust stability
and control synthesis for uncertain switched neutral systems with mixed
delays. Applied Mathematics and Computation, Vol. 202, No. 2, pp.828-
839, 2008.
[26] L. Xie, Output feedback H∞ control of systems with parameter uncertainty.
International Journal of Control, Vol. 63, No. 4, pp.741-750,
1996.
[27] S. Boyd , L.-E. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix
inequalities in systems and control theory. Philadelphia: SIAM, 1994.
[28] K. Gu, V.-L. Kharitonov, J. Chen, Stability of time-delay systems.
Birkhauser, Basel, 2003.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:64367", author = "Lianglin Xiong and Shouming Zhong and Mao Ye", title = "Delay-dependent Stability Analysis for Uncertain Switched Neutral System", abstract = "This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.
", keywords = "Switched neutral system, exponential stability, multiple Lyapunov functional, dwell time technique, time-dependent switching rule.", volume = "3", number = "9", pages = "752-8", }
