×

Input/output-to-state stability and state-norm estimators for switched nonlinear systems. (English) Zbl 1257.93088

Summary: In this paper, the concepts of input/output-to-state stability (IOSS) and state-norm estimators are considered for switched nonlinear systems under average dwell-time switching signals. We show that when the average dwell-time is large enough, a switched system is IOSS if all of its constituent subsystems are IOSS. Moreover, under the same conditions, a non-switched state-norm estimator exists for the switched system. Furthermore, if some of the constituent subsystems are not IOSS, we show that still IOSS can be established for the switched system, if the activation time of the non-IOSS subsystems is not too big. Again, under the same conditions, a state-norm estimator exists for the switched system. However, in this case, the state-norm estimator is a switched system itself, consisting of two subsystems. We show that this state-norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for.

MSC:

93D25 Input-output approaches in control theory
93E10 Estimation and detection in stochastic control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C10 Nonlinear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Angeli, D.; Sontag, E. D., Forward completeness, unboundedness observability, and their Lyapunov characterizations, Systems & Control Letters, 38, 209-217 (1999) · Zbl 0986.93036
[2] Astolfi, A.; Praly, L., Global complete observability and output-to-state stability imply the existence of a globally convergent observer, Mathematics of Control Signals and Systems, 18, 1, 32-65 (2006) · Zbl 1105.93017
[3] García, R.A., & Mancilla-Aguilar, J.L. (2002). State-norm estimation of switched nonlinear systems. In Proceedings of the American control conference; García, R.A., & Mancilla-Aguilar, J.L. (2002). State-norm estimation of switched nonlinear systems. In Proceedings of the American control conference
[4] Hespanha, J.P., & Morse, A.S. (1999). Stability of switched systems with average dwell-time. In Proceedings of the 38th IEEE conference on decision and control; Hespanha, J.P., & Morse, A.S. (1999). Stability of switched systems with average dwell-time. In Proceedings of the 38th IEEE conference on decision and control
[5] Krichman, M.; Sontag, E. D.; Wang, Y., Input-output-to-state stability, SIAM Journal on Control and Optimization, 39, 6, 1874-1928 (2001) · Zbl 1005.93044
[6] Liberzon, D., Switching in systems and control (2003), Birkhäuser: Birkhäuser Boston, MA · Zbl 1036.93001
[7] Mancilla-Aguilar, J. L.; García, R.; Sontag, E.; Wang, Y., On the representation of switched systems with inputs by perturbed control systems, Nonlinear Analysis, 60, 1111-1150 (2005) · Zbl 1066.93034
[8] Morse, A. S., Supervisory control of families of linear set-point controllers — part I: exact matching, IEEE Transactions on Automatic Control, 41, 1413-1431 (1996) · Zbl 0872.93009
[9] Muñoz de la Peña, D.; Christofides, P. D., Stability of nonlinear asynchronous systems, Systems & Control Letters, 57, 465-473 (2008) · Zbl 1154.93027
[10] Praly, L., & Astolfi, A. (2005). Global asymptotic stabilization by output feedback under a state norm detectability assumption. In Proceedings of the 44th IEEE conference on decision and control, and the European control conference; Praly, L., & Astolfi, A. (2005). Global asymptotic stabilization by output feedback under a state norm detectability assumption. In Proceedings of the 44th IEEE conference on decision and control, and the European control conference
[11] Praly, L.; Wang, Y., Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability, Mathematics of Control Signals and Systems, 9, 1-33 (1996) · Zbl 0869.93040
[12] Sanfelice, R.G. (2010). Results on input-to-output and input-output-to-state stability for hybrid systems and their interconnections. In Proceedings of the 49th IEEE conference on decision and control; Sanfelice, R.G. (2010). Results on input-to-output and input-output-to-state stability for hybrid systems and their interconnections. In Proceedings of the 49th IEEE conference on decision and control
[13] Sontag, E. D.; Wang, Y., On characterizations of the input-to-state stability property, Systems & Control Letters, 24, 351-359 (1995) · Zbl 0877.93121
[14] Sontag, E. D.; Wang, Y., Output-to-state stability and detectability of nonlinear systems, Systems & Control Letters, 29, 279-290 (1997) · Zbl 0901.93062
[15] Vu, L.; Chatterjee, D.; Liberzon, D., Input-to-state stability of switched systems and switching adaptive control, Automatica, 43, 639-646 (2007) · Zbl 1261.93049
[16] Xie, W.; Wen, C.; Li, Z., Input-to-state stabilization of switched nonlinear systems, IEEE Transactions on Automatic Control, 46, 7, 1111-1116 (2001) · Zbl 1010.93089
[17] Zhai, G.; Hu, B.; Yasuda, K.; Michel, A. N., Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach, International Journal of Systems Science, 32, 8, 1055-1061 (2001) · Zbl 1022.93043
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.