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Sampled-data-based stabilization of switched linear neutral systems. (English) Zbl 1344.93067

Summary: With the development of digital control technology, sampled-data control shows its prominent superiority for most practical industries. In the framework of sampled-data control, this paper studies the stabilization problem for a class of switched linear neutral systems meanwhile taking into account asynchronous switching. By utilizing the relationship between the sampling period and the dwell time of switched neutral systems, a bond between the sampling period and the average dwell time is revealed to form a switching condition, under which and certain control gains conditions exponential stability of the closed-loop systems is guaranteed. A simple example is given to demonstrate the effectiveness of the proposed method.

MSC:

93C57 Sampled-data control/observation systems
93D20 Asymptotic stability in control theory
83C30 Asymptotic procedures (radiation, news functions, \(\mathcal{H} \)-spaces, etc.) in general relativity and gravitational theory
93C05 Linear systems in control theory
Full Text: DOI

References:

[1] Blankenship, G.; Papanicolaou, G. C., Stability and control of stochastic systems with wideband noise disturbances, SIAM Journal on Applied Mathematics, 42, 3, 437-476 (1978) · Zbl 0392.93040
[2] Branicky, M., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, 43, 4, 475-482 (1998) · Zbl 0904.93036
[3] Chen, T.; Francis, B. A., Input-output stability of sampled-data systems, IEEE Transactions on Automatic Control, 36, 50-58 (1991) · Zbl 0723.93059
[4] Chen, T.; Francis, B. A., Optimal sampled-data control systems (1995), Springer · Zbl 0847.93040
[5] Chen, W.; Zheng, W., Delay-independent minimum dwell time for exponential stability of uncertain switched delay systems, IEEE Transactions on Automatic Control, 55, 10, 2406-2413 (2010) · Zbl 1368.93493
[6] Feng, L.; Song, Y., Stability condition for sampled data based control of linear continuous switched systems, Systems & Control Letters, 60, 10, 787-797 (2011) · Zbl 1226.93090
[7] Fu, J.; Ma, R.; Chai, T., Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers, Automatica, 54, 360-373 (2015) · Zbl 1318.93081
[10] Hu, L.; Lam, J.; Cao, Y.; Shao, H., A linear matrix inequality approach to robust \(H_2\) sampled-data control for linear uncertain systems, IEEE Transactions on Systems, Man and Cybernetics, 33, 149-155 (2003)
[11] Krishnasamy, R.; Balasubramaniam, P., A descriptor system approach to the delay-dependent exponential stability analysis for switched neutral systems with nonlinear perturbations, Nonlinear Analysis. Hybrid Systems, 15, 23-26 (2015) · Zbl 1307.34115
[12] Krishnasamy, R.; Balasubramaniam, P., Stabilisation analysis for switched neutral systems based on sampled-data control, International Journal of Systems Science, 46, 14, 2531-2546 (2015) · Zbl 1332.93320
[13] Lian, J.; Ge, Y.; Han, M., Stabilization for switched stochastic neutral systems under asynchronous switching, Information Sciences, 222, 501-508 (2013) · Zbl 1293.93611
[14] Liberzon, D., Switched in systems and control (2003), Birkhauser: Birkhauser Boston · Zbl 1036.93001
[15] Liberzon, D., Finite data-rate feedback stabilization of switched and hybrid linear systems, Automatica, 50, 2, 409-420 (2014) · Zbl 1364.93648
[16] Lien, C.; Chen, J.; Yu, K.; Chung, L., Robust delay-dependent \(H_\infty\) control for uncertain switched time-delay systems via sampled-data state feedback input, Computers and Mathematics with Applications, 64, 5, 1187-1196 (2012) · Zbl 1356.93027
[17] Lin, H.; Antsaklis, P., Stability and stabilizability of switched linear systems: a survey of recent results, IEEE Transactions on Automatic Control, 54, 308-322 (2009) · Zbl 1367.93440
[18] Liu, D.; Liu, X.; Zhong, S., Delay-dependent robust stability and control synthesis for uncertain switched neutral systems with mixed delays, Applied Mathematics and Computation, 202, 2, 828-839 (2008) · Zbl 1143.93020
[19] Li, T.; Zhao, J.; Qi, Y., Switching design of stabilizing switched neutral systems with application to lossless transmission lines, IET Control Theory & Applications, 17, 2082-2091 (2014)
[20] Sun, X.; Du, S.; Shi, P.; Wang, W.; Wang, L., Input-to-state stability for nonlinear systems with large delay period based on switching techniques, IEEE Transactions on Circuits and Systems. I. Regular Papers, 61, 6, 1789-1800 (2014)
[22] Sun, Z.; Ge, S., Analysis and synthesis of switched linear control systems, Automatica, 41, 2, 181-195 (2005) · Zbl 1074.93025
[23] Sun, X.; Liu, G.; David, R.; Wang, W., Stability of systems with controller failure and time-varying delay, IEEE Transactions on Automatic Control, 53, 941-953 (2008) · Zbl 1367.93452
[24] Sun, X.; Zhao, J.; Hill, D., Stability and \(L_2\)-gain analysis for switched delay systems: A delay-dependent method, Automatica, 42, 10, 1769-1774 (2006) · Zbl 1114.93086
[25] Wang, R.; Xing, J.; Zhou, C.; Wang, P.; Yang, Q., Finite-time asynchronously switched control of switched systems with sampled data feedback, Circuits, Systems, and Signal Processing, 33, 3713-3738 (2014) · Zbl 1342.93077
[26] Wang, Y.; Zhao, J.; Jiang, B., Stabilization of a class of switched linear neutral systems under asynchronous switching, IEEE Transactions on Automatic Control, 58, 2114-2119 (2013) · Zbl 1369.93511
[27] Wu, F.; Dong, K., Gain-scheduling control of LFT systems using parameter-dependent Lyapunov function, Automatica, 42, 39-50 (2006) · Zbl 1121.93067
[28] Xiang, Z.; Sun, Y.; Chen, Q., Robust reliable stabilization of uncertain switched neutral systems with delayed switching, Applied Mathematics and Computation, 217, 23, 9835-9844 (2011) · Zbl 1227.34075
[29] Xiang, Z.; Sun, Y.; Chen, Q., Stabilization for a class of switched neutral systems under asynchronous switching, Transactions of the Institute of Measurement and Control, 34, 739-801 (2012)
[30] Xiang, Z.; Sun, Y.; Mahmoud, M., Robust finite-time \(H_\infty\) control for a class of uncertain switched neutral systems, Communications in Nonlinear Science and Numerical Simulation, 17, 4, 1766-1778 (2012) · Zbl 1239.93036
[31] Xiong, L.; Zhong, S.; Ye, M.; Wu, S., New stability and stabilization for switched neutral control systems, Chaos, Solitons & Fractals, 42, 3, 1800-1811 (2009) · Zbl 1198.93187
[32] Zhai, G.; Hu, B.; Yasuda, K.; Michel, A., Disturbance attenuation properties of time-controlled switched systems, Journal of the Franklin Institute. Engineering and Applied Mathematics, 338, 765-779 (2001) · Zbl 1022.93017
[33] Zhang, L.; Gao, H., Asynchonously switched control of switched linear systems with average dwell time, Automatica, 46, 5, 953-958 (2010) · Zbl 1191.93068
[34] Zhang, Y.; Liu, X.; Zhu, H.; Zhong, S., Stability analysis and control synthesis for a class of switched neutral systems, Applied Mathematics and Computation, 190, 2, 1258-1266 (2007) · Zbl 1117.93062
[35] Zhang, W.; Yu, L., Stability analysis for discrete-time switched time-delay systems, Automatica, 45, 10, 2265-2271 (2009) · Zbl 1179.93145
[36] Zhang, D.; Yu, L., Exponential stability analysis for neutral switched systems with interval time-varying mixed delays and nonlinear perturbations, Nonlinear Analysis. Hybrid Systems, 6, 2, 775-786 (2012) · Zbl 1238.93090
[37] Zhang, L.; Zhuang, S.; Shi, P., Non-weighted quasi-time-dependent \(H_\infty\) filtering for switched linear systems with persistent dwell-time, Automatica, 54, 201-209 (2015) · Zbl 1318.93094
[38] Zhang, L.; Zhuang, S.; Shi, P.; Zhu, Y., Uniform tube based stabilization of switched linear systems with mode-dependent persistent dwell-time, IEEE Transactions on Automatic Control, 60, 2994-2999 (2015) · Zbl 1360.93625
[39] Zhao, J.; Hill, D., On stability, \(L_2\)-gain and \(H_\infty\) control for switched systems, Automatica, 44, 1220-1232 (2008) · Zbl 1283.93147
[40] Zhao, X.; Shi, P.; Zhang, L., Asynchronously switched control of a class of slowly switched linear systems, Systems & Control Letters, 61, 12, 1151-1156 (2012) · Zbl 1255.93119
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