zbMATH — the first resource for mathematics

Asynchronously switched control of a class of slowly switched linear systems. (English) Zbl 1255.93119
Summary: The stabilization problem for a class of switched linear systems with Average Dwell Time (ADT) switching is reinvestigated in this paper. State-feedback controllers are designed, which takes the more practical case, asynchronous switching, into account, where the so-called ”asynchronous switching” indicates that the switchings between the controllers and the system modes are in the presence of a time delay. By combining the asynchronous switching, an improved stabilization approach is given, and existence conditions of the controllers associated with the corresponding ADT switching are formulated in terms of a set of linear matrix inequalities. A numerical example is given to show the validity and potential of the obtained theoretical results.

93D15 Stabilization of systems by feedback
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C05 Linear systems in control theory
93B52 Feedback control
Full Text: DOI
[1] Artstein, Z.; Ronen, J., On stabilization of switched linear systems, Systems control lett., 57, 11, 919-926, (2008) · Zbl 1149.93337
[2] El-Farra, N.; Mhaskar, P.; Christofides, P., Output feedback control of switched nonlinear systems using multiple Lyapunov functions, Systems control lett., 54, 12, 1163-1182, (2005) · Zbl 1129.93497
[3] Wang, D.; Wang, W.; Shi, P., Robust fault detection for switched linear systems with state delays, IEEE trans. syst. man cybern. B, 39, 3, 800-805, (2009)
[4] Sun, X.; Zhao, J.; Hill, D.J., Stability and \(L_2\)-gain analysis for switched delay systems: a delay-dependent method, Automatica, 42, 10, 1769-1774, (2006) · Zbl 1114.93086
[5] Gao, H.J.; Lam, J.; Wang, C.H., Model simplification for switched hybrid systems, Systems control lett., 55, 12, 1015-1021, (2006) · Zbl 1120.93311
[6] Zhang, G.; Han, C.; Guan, Y.; Wu, L., Exponential stability analysis and stabilization of discrete-time nonlinear switched systems with time delays, Int. J. inno. comput. inf. control, 8, 3, 1973-1986, (2012)
[7] Liu, Q.; Wang, W.; Wang, D., New results on model reduction for discrete-time switched systems with time delay, Int. J. innov. comput. inf. control, 8, 5, 3431-3440, (2012)
[8] Wu, Z.; Shi, P.; Su, H.; Chu, J., Delay-dependent stability analysis for switched neural networks with time-varying delay, IEEE trans. syst. man cybern. B, 41, 6, 1522-1530, (2011)
[9] Zhang, H.; Liu, Z.; Huang, G., Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via sc technique, IEEE trans. syst. man cybern. B, 40, 6, 180-1491, (2010)
[10] Tse, C.K.; Di Bernardo, M., Complex behavior in switching power converters, IEEE proc., 90, 5, 768-781, (2002)
[11] Pellanda, P.; Apkarian, P.; Tuan, H., Missile autopilot design via a multi-channel LFT/LPV control method, Int. J. robust nonlinear control, 12, 1, 1-20, (2002) · Zbl 1031.93127
[12] Persisa, C.; Santis, R.; Morse, A., Switched nonlinear systems with state-dependent Dwell-time, Systems control lett., 50, 4, 291-302, (2003) · Zbl 1157.93510
[13] Shi, P.; Boukas, E.K.; Agarwal, R.K., Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay, IEEE trans. automat. control, 44, 11, 2139-2144, (1999) · Zbl 1078.93575
[14] Ishii, H.; Basar, T.; Tempo, R., Randomized algorithms for synthesis of switching rules for multimodal systems, IEEE trans. automat. control, 50, 6, 754-767, (2005) · Zbl 1365.93400
[15] Xu, H.; Teo, K.L., Exponential stability with \(L_2\)-gain condition of nonlinear impulsive switched systems, IEEE trans. automat. control, 55, 10, 2429-2433, (2010) · Zbl 1368.93614
[16] Sun, X.; Wang, W.; Liu, G.; Zhao, J., Stability analysis for linear switched systems with time-varying delay, IEEE trans. syst. man cybern. B, 38, 2, 528-533, (2008)
[17] Fainshil, L.; Margaliot, M.; Chigansky, P., On the stability of positive linear switched systems under arbitrary switching laws, IEEE trans. automat. control, 54, 4, 897-899, (2009) · Zbl 1367.93431
[18] Zhao, X.; Zhang, L.; Shi, P.; Liu, M., Stability and stabilization of switched linear systems with mode-dependent average Dwell time, IEEE trans. automat. control, 57, 7, 1809-1815, (2012) · Zbl 1369.93290
[19] Zhang, W.; Yu, L., Stability analysis for discrete-time switched time-delay systems, Automatica, 45, 10, 2265-2271, (2009) · Zbl 1179.93145
[20] Mahmoud, M.S.; Shi, P., Robust stability, stabilization and \(H_\infty\) control of time-delay systems with Markovian jump parameters, Int. J. robust nonlinear control, 13, 755-784, (2003) · Zbl 1029.93063
[21] Lin, H.; Antsaklis, P.J., Stability and stabilizability of switched linear systems: a survey of recent results, IEEE trans. automat. control, 54, 2, 308-322, (2009) · Zbl 1367.93440
[22] Zhao, X.; Zhang, L.; Shi, P.; Liu, M., Stability of switched positive linear systems with average Dwell time switching, Automatica, 46, 6, 1132-1137, (2012) · Zbl 1244.93129
[23] Zhang, L.; Shi, P., \(l_2 - l_\infty\) model reduction for switched LPV systems with average Dwell time, IEEE trans. automat. control, 53, 10, 2443-2448, (2008) · Zbl 1367.93115
[24] Cao, M.; Morse, A.S., Dwell-time switching, Systems control lett., 59, 1, 57-65, (2010) · Zbl 1186.93005
[25] Zhang, L.; Shi, P., Stability, \(l_2\)-gain and asynchronous \(H_\infty\) control of discrete-time switched systems with average Dwell time, IEEE trans. automat. control, 54, 9, 2193-2200, (2009)
[26] Wang, M.; Zhao, J., \(L_2\)-gain analysis and control synthesis for a class of uncertain switched nonlinear systems, Acta automat. sinica, 35, 11, 1459-1464, (2009)
[27] Wang, L.; Shao, C., Exponential stabilisation for time-varying delay system with actuator faults: an average Dwell time method, Internat. J. control, 41, 4, 435-445, (2010) · Zbl 1301.93137
[28] Attia, S.B.; Salhi, S.; Ksouri, M., Static switched output feedback stabilization for linear discrete-time switched systems, Int. J. inno. comput. inf. control, 8, 5, 3203-3213, (2012)
[29] Xiong, J.L.; Lam, J., Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers, Automatica, 42, 5, 747-753, (2006) · Zbl 1137.93421
[30] Mhaskar, P.; El-Farra, N.H.; Christofides, P.D., Robust predictive control of switched systems: satisfying uncertain schedules subject to state and control constraints, Int. J. adapt. control signal process., 22, 2, 161-179, (2008) · Zbl 1241.93019
[31] L. Hetel, J. Daafouz, C. Iung, Stability analysis for discrete time switched systems with temporary uncertain switching signal, in: Proc. 46th IEEE Conf. Decision and Control, New Orleans, LA, USA, 2007, pp. 5623-5628.
[32] Zhang, L.; Gao, H., Asynchronously switched control of switched linear systems with average Dwell time, Automatica, 46, 5, 953-958, (2010) · Zbl 1191.93068
[33] Vu, L.; Morgansen, K., Stability of feedback switched systems with state and switching delays, IEEE trans. automat. control, 55, 10, 2385-2390, (2010) · Zbl 1368.93573
[34] Zhang, L.; Cui, N.; Liu, M.; Zhao, Y., Asynchronous filtering of discrete-time switched linear systems with average Dwell time, IEEE trans. circuits syst. I, 58, 5, 1109-1118, (2011)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.