\(p\)th moment exponential stability of stochastic PWM feedback systems with time-varying delays. (English) Zbl 1325.93055

Summary: This paper further studies the \(p\)th moment exponential stability of stochastic Pulse-Width-Modulated (PWM) feedback systems with distributed time-varying delays. We establish several globally exponential stability criteria for such PWM feedback systems by using Lyapunov-Krasovskii functional and then present an upper bound of the parameter of PWM when the system is stable and such system has stronger anti-interference performance than the system without time-varying delays. Furthermore, we present two examples to show the effectiveness and conservativeness of the theoretical results.


93E15 Stochastic stability in control theory
93B52 Feedback control
62H10 Multivariate distribution of statistics
93D30 Lyapunov and storage functions
Full Text: DOI


[1] I. Takahashi, “A new control of PWM inverter wave form for minimum loss operation of an induction motor drive,” IEEE Transactions on Industry Applications, vol. 21, no. 4, pp. 580-587, 1985. · doi:10.1109/TIA.1985.349713
[2] S.-Y. Choe, J.-G. Lee, J.-W. Ahn, and S.-H. Baek, “Integrated modeling and control of a PEM fuel cell power system with a PWM DC/DC converter,” Journal of Power Sources, vol. 164, no. 2, pp. 614-623, 2007. · doi:10.1016/j.jpowsour.2006.10.082
[3] J.-C. Bor and C.-Y. Wu, “Realization of the CMOS pulsewidth-modulation (PWM) neural network with on-chip learning,” IEEE Transactions on Circuits and Systems II, vol. 45, no. 1, pp. 96-107, 1998. · doi:10.1109/82.659460
[4] Z. Hui and B. Michael, “A new partly unsymmetrical PWM technique for harmopnic compensators,” in Proceedings of the 11th European Conference on Power Electronics and Applications (EPE ’05), Dresdnen, Germany, September 2005. · doi:10.1109/82.659460
[5] N. Bodo, M. Jones, and E. Levi, “A PWM method for seven- and nine-phase open-end winding motor drives,” Mathematics and Computers in Simulation. In press. · doi:10.1109/82.659460
[6] G. J. Murphy and S. H. Wu, “A stability criterion for pulse-width-modulated feedback control systems,” IEEE Transactions on Automatic Control, vol. 9, pp. 434-441, 1964. · doi:10.1109/TAC.1964.1105786
[7] A. Balestrino, A. Eisinberg, and L. Sciavicco, “A generalised approach to the stability analysis of PWM feedback control systems,” Journal of the Franklin Institute, vol. 298, no. 1, pp. 45-58, 1974. · Zbl 0307.93027 · doi:10.1016/0016-0032(74)90088-X
[8] R. A. Skoog, “On the stability of pulse width modulated feedback systems,” IEEE Transactions on Automatic Control, vol. 13, no. 5, pp. 532-538, 1968. · doi:10.1109/TAC.1968.1098987
[9] A. Halanay, “Positive definite kernels and stability of automatic systems,” Revue Roumaine de Mathématique Pures et Appliquées, vol. 9, no. 8, pp. 751-765, 1964 (Russian). · Zbl 0129.06804
[10] V. M. Popov, “On absolute stability of nonlinear systems of automatic regulation,” Avtomatika i Telemekhanika, vol. 22, no. 8, pp. 961-979, 1961. · Zbl 0107.29601
[11] S. C. Gupta and E. I. Jury, “Statistical study of pulse-width modulated control systems,” Journal of the Franklin Institute, vol. 273, no. 4, pp. 292-321, 1962. · doi:10.1016/S0016-0032(62)91131-6
[12] L. Hou and A. N. Michel, “Moment stability of pulse-width-modulated feedback systems subjected to random disturbances,” in Proceedings of the 39th IEEE Confernce on Decision and Control, pp. 2343-2348, Sydney, Australia, December 2000.
[13] L. Hou and A. N. Michel, “Moment stability of discontinuous stochastic dynamical systems,” in Proceedings of the Americal Control Conference, vol. 6, pp. 3807-3811, Chicago, Ill, USA, June 2000. · doi:10.1109/ACC.2000.876934
[14] S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. · Zbl 0816.93004
[15] P. Cheng, F. Deng, and Y. Peng, “Robust exponential stability and delayed-state-feedback stabilization of uncertain impulsive stochastic systems with time-varying delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 12, pp. 4740-4752, 2012. · Zbl 1263.93232 · doi:10.1016/j.cnsns.2012.03.038
[16] W. Su and Y. Chen, “Global robust exponential stability analysis for stochastic interval neural networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2293-2300, 2009. · Zbl 1221.93215 · doi:10.1016/j.cnsns.2008.05.001
[17] Y. Sun and J. Cao, “pth moment exponential stability of stochastic recurrent neural networks with time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1171-1185, 2007. · Zbl 1196.60125 · doi:10.1016/j.nonrwa.2006.06.009
[18] C. Li, T. Huang, G. Feng, and G. Chen, “Exponential stability of time-controlled switching systems with time delay,” Journal of the Franklin Institute, vol. 349, no. 1, pp. 216-233, 2012. · Zbl 1254.93136 · doi:10.1016/j.jfranklin.2011.10.016
[19] H. Huang and G. Feng, “Delay-dependent stability for uncertain stochastic neural networks with time-varying delay,” Physica A, vol. 381, no. 1-2, pp. 93-103, 2007. · doi:10.1016/j.physa.2007.04.020
[20] C. Li, C. Li, X. Liao, and T. Huang, “Impulsive effects on stability of high-order BAM neural networks with time delays,” Neurocomputing, vol. 74, no. 10, pp. 1541-1550, 2011. · Zbl 06017177 · doi:10.1016/j.neucom.2010.12.028
[21] J. Tian, S. Zhong, and Y. Wang, “Improved exponential stability criteria for neural networks with time-varying delays,” Neurocomputing, vol. 97, no. 15, pp. 164-173, 2012. · Zbl 06075828 · doi:10.1016/j.neucom.2012.05.018
[22] Z. Wu, H. Su, J. Chu, and W. Zhou, “New results on robust exponential stability for discrete recurrent neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 13-15, pp. 3337-3342, 2009. · Zbl 05721119 · doi:10.1016/j.neucom.2009.01.010
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