New Stabilization for Switched Neutral Systems with Perturbations
This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.
[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] J.-C. Geromel, P. Colaneri, Stability and stabilization of continuous-time
switched linear systems, SIAM Journal on Control and Optimization
Vol. 45, No. 5, pp. 1915-1930, 2006.
[27] L. Xie, Output feedback control of systems with parameter uncertainty,
International Journal of Control, Vol. 63, No. 4, pp.741-750, 1996.
[28] S. Boyd , L.-E. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix
inequalities in systems and control theory. Philadelphia: SIAM, 1994.
[29] R. Rockafellar, Convex Analysis, Princeton: Princeton Press, 1970.
[30] K.-M. Garg, Theory of Differentiation: A Unified Theory of differentiation
via new derivate theorems and new derivatives, Wiley-Interscience,
New York, 1998.
[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] J.-C. Geromel, P. Colaneri, Stability and stabilization of continuous-time
switched linear systems, SIAM Journal on Control and Optimization
Vol. 45, No. 5, pp. 1915-1930, 2006.
[27] L. Xie, Output feedback control of systems with parameter uncertainty,
International Journal of Control, Vol. 63, No. 4, pp.741-750, 1996.
[28] S. Boyd , L.-E. Ghaoui, E. Feron, V. Balakrishnan, Linear matrix
inequalities in systems and control theory. Philadelphia: SIAM, 1994.
[29] R. Rockafellar, Convex Analysis, Princeton: Princeton Press, 1970.
[30] K.-M. Garg, Theory of Differentiation: A Unified Theory of differentiation
via new derivate theorems and new derivatives, Wiley-Interscience,
New York, 1998.
@article{"International Journal of Information, Control and Computer Sciences:53199", author = "Lianglin Xiong and Shouming Zhong and Mao Ye", title = "New Stabilization for Switched Neutral Systems with Perturbations", abstract = "This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.
", keywords = "Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.", volume = "3", number = "9", pages = "2189-8", }
