New Stabilization for Switched Neutral Systems with Perturbations
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33122
New Stabilization for Switched Neutral Systems with Perturbations

Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331509

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1659

References:


[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.