Interval stability/stabilization for linear stochastic switched systems with time-varying delay. (English) Zbl 1510.93343
Summary: In this paper, the interval stability/stabilization of linear stochastic switched time-varying delay systems are considered. Firstly, the interval stability is defined and the sufficient conditions for the interval stability of linear stochastic switched systems are addressed. Different from current stability conditions, the interval stability criterion can make more accurate judgment than stability of linear stochastic switched time-varying delay systems. Secondly, the criterion of interval stabilization is gained by linear matrix inequalities, which can not merely ensure the stability of the system, but also accelerate or slow down the convergence of the system. Finally, the validity of the theoretical results is verified by a digital simulation and water quality preservation problem.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93D20 | Asymptotic stability in control theory |
| 93B36 | \(H^\infty\)-control |
| 34A08 | Fractional ordinary differential equations |
Keywords:
linear stochastic switched systems; interval stability; time-varying delay; interval stabilizationReferences:
| [1] | Morselli, R.; Zanasi, R.; Ferracin, P., Modelling and simulation of static and coulomb friction in a class of automotive systems, Int. J. Control, 79, 5, 508-520 (2006) · Zbl 1117.93009 |
| [2] | Li, M.; Chen, Y., Robust adaptive sliding mode control for switched networked control systems with disturbance and faults, IEEE Trans. Ind. Inform., 15, 1, 193-204 (2019) |
| [3] | Li, L.; Song, L.; Li, T.; Fu, J., Event-triggered output regulation for networked flight control system based on an asynchronous switched system approach, IEEE Trans. Syst. Man Cybern. Syst., 1-10 (2020) |
| [4] | Liberzon, D., Switching in Systems and Control (2003), Birkhauser: Birkhauser Boston · Zbl 1036.93001 |
| [5] | Zhang, J.; Zhang, R.; Cai, X.; Jia, X., A novel approach to control synthesis of positive switched systems, IET Control Theory Appl., 11, 18, 3396-3403 (2017) |
| [6] | Zhang, J.; Zhao, X.; Zhang, R.; Zhou, S., Dual approach to stability and stabilisation of uncertain switched positive systems, Int. J. Syst. Sci., 48, 4, 873-884 (2017) · Zbl 1358.93134 |
| [7] | Zhang, J.; Li, M.; Zhang, R., New computation method for average dwell time of general switched systems and positive switched systems, IET Control Theory Appl., 12, 16, 2263-2268 (2018) |
| [8] | Zhao, X.; Shi, P.; Yin, Y.; Nguang, S. K., New results on stability of slowly switched systems: a multiple discontinuous Lyapunov function approach, IEEE Trans. Autom. Control, 62, 7, 3502-3509 (2017) · Zbl 1370.34108 |
| [9] | Wu, X.; Tang, Y.; Cao, J.; Mao, X., Stability analysis for continuous-time switched systems with stochastic switching signals, IEEE Trans. Autom. Control, 63, 9, 3083-3090 (2018) · Zbl 1423.93407 |
| [10] | Biswas, D.; Banerjee, T., A simple chaotic and hyperchaotic time-delay system: design and electronic circuit implementation, Nonlinear Dyn., 83, 4, 2331-2347 (2016) |
| [11] | Liu, Z.; Wu, Y., Universal strategies to explicit adaptive control of nonlinear time-delay systems with different structures, Automatica, 89, 89, 151-159 (2018) · Zbl 1387.93101 |
| [12] | Ma, R.; Ma, M.; Li, J.; Wu, J. F.C., Standard \(h_\infty\) performance of switched delay systems under minimum dwell time switching, J. Franklin Inst., 356, 6, 3443-3456 (2019) · Zbl 1411.93063 |
| [13] | Li, S.; Xiang, Z.; Karimi, H. R., Stability and \(l_1\)-gain controller design for positive switched systems with mixed time-varying delays, Appl. Math. Comput., 222, 507-518 (2013) · Zbl 1328.93215 |
| [14] | Li, S.; Xiang, Z., Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays, Appl. Math. Comput., 372, 124981 (2020) · Zbl 1433.93083 |
| [15] | Jin, S.; Pang, Y.; Zhou, X.; Yan, A.; Wang, W.; Hu, W., Robust finite-time control and reachable set estimation for uncertain switched neutral systems with time delays and input constraints, Appl. Math. Comput., 407, 126321 (2021) · Zbl 1510.93045 |
| [16] | Li, Y.; Sun, Y.; Meng, F.; Tian, Y., Exponential stabilization of switched time-varying systems with delays and disturbances, Appl. Math. Comput., 324, 131-140 (2018) · Zbl 1426.34101 |
| [17] | Luo, S.; Deng, F.; Chen, W., Multiple switching-time-dependent discretized Lyapunov functions/functionals methods for stability analysis of switched time-delay stochastic systems, J. Frankl. Inst., 355, 2, 949-964 (2018) · Zbl 1384.93153 |
| [18] | Zhou, B.; Luo, W., Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems, Automatica, 89, 89, 382-391 (2018) · Zbl 1388.93103 |
| [19] | Hu, Z.; Deng, F.; Shi, P.; Luo, S.; Xing, M., Robust exponential stability of uncertain stochastic systems with probabilistic time-varying delays, Int. J. Robust Nonlinear Control, 28, 9, 3273-3291 (2018) · Zbl 1396.93127 |
| [20] | Xiang, Z.; Chen, G., Stability analysis and robust control of switched stochastic systems with time-varying delay, J. Appl. Math., 2012, 2012, 1-17 (2012) · Zbl 1243.93030 |
| [21] | Rajchakit, M.; Rajchakit, G., Mean square exponential stability of stochastic switched system with interval time-varying delays, Abstr. Appl. Anal., 2012, 1-12 (2012) · Zbl 1246.93081 |
| [22] | Chen, H.; Lim, C. C.; Shi, P., Stability analysis for stochastic neutral switched systems with time-varying delay, SIAM J. Control Optim., 59, 1, 24-49 (2021) · Zbl 1471.34138 |
| [23] | Jia, H.; Xiang, Z.; Karimi, H., Robust reliable passive control of uncertain stochastic switched time-delay systems, Appl. Math. Comput., 231, 254-267 (2014) · Zbl 1410.93109 |
| [24] | Sun, S.; Wang, Y.; Zhang, H.; Sun, J., Multiple intermittent fault estimation and tolerant control for switched T-S fuzzy stochastic systems with multiple time-varying delays, Appl. Math. Comput., 377, 125114 (2020) · Zbl 1508.93308 |
| [25] | Sakthivel, R.; Saravanakumar, T.; Kaviarasan, B.; Anthoni, S. M., Dissipativity based repetitive control for switched stochastic dynamical systems, Appl. Math. Comput., 291, 340-353 (2016) · Zbl 1410.93150 |
| [26] | Huang, X.; Liu, Y.; Wang, Y.; Zhou, J.; Fang, M.; Wang, Z., \( L_2 - L_\infty\) consensus of stochastic delayed multi-agent systems with ADT switching interaction topologies, Appl. Math. Comput., 368, 124800 (2020) · Zbl 1433.93005 |
| [27] | Chilali, M.; Gahinet, P.; Apkarian, P., Robust pole placement in LMI regions, IEEE Trans. Autom. Control, 44, 12, 2257-2270 (1999) · Zbl 1136.93352 |
| [28] | Klinshov, V. V.; Kirillov, S.; Kurths, J.; Nekorkin, V. I., Interval stability for complex systems, New J. Phys., 20, 4, 43040 (2018) · Zbl 07858156 |
| [29] | Zhang, W.; Xie, L., Interval stability and stabilization of linear stochastic systems, IEEE Trans. Autom. Control, 54, 4, 810-815 (2009) · Zbl 1367.93577 |
| [30] | Zhang, H.; Xia, J.; Shen, H.; Zhang, B.; Wang, Z., pth moment regional stability/stabilization and generalized pole assignment of linear stochastic systems: based on the generalized-representation method, Int. J. Robust Nonlinear Control, 30, 8, 3234-3249 (2020) · Zbl 1466.93175 |
| [31] | Zhang, H.; Xia, J.; Zhang, Y.; Shen, H.; Wang, Z., pth moment D-stability/stabilization of linear discrete-time stochastic systems, Sci. China Inf. Sci., 65, 3, 1-3 (2021) |
| [32] | Zhang, H.; Xia, J.; Park, J. H.; Sun, W.; Zhuang, G., Interval stability and interval stabilization of linear stochastic systems with time-varying delay, Int. J. Robust Nonlinear Control, 31, 6, 2334-2347 (2021) · Zbl 1526.93275 |
| [33] | Zhang, W.; Xie, L.; Chen, B., Stochastic \(H_2 / H_\infty\) Control-A Nash Game Approach (2017), CRC Press · Zbl 1403.93003 |
| [34] | Zong, X.; Yin, G.; Wang, L.; Li, T.; Zhang, J., Stability of stochastic functional differential systems using degenerate Lyapunov functionals and applications, Automatica, 91, 197-207 (2018) · Zbl 1387.93177 |
| [35] | Jin, C.; Li, L.; Wang, R.; Wang, Q., Output regulation for stochastic delay systems under asynchronous switching with dissipativity, Int. J. Control, 94, 2, 548-557 (2021) · Zbl 1461.93487 |
| [36] | Chen, G.; Xiang, Z.; Karimi, H. R., Observer-based robust control for switched stochastic systems with time-varying delay, Abstr. Appl. Anal., 2013, 1-12 (2013) · Zbl 1291.93116 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
