Abstract
This chapter first investigates the stability and \(l_2\)-gain analysis problems for a class of discrete-time switched systems with average dwell time (ADT) switching by allowing the Lyapunov-like functions to increase during the running time of subsystems. The obtained results then facilitate the studies on the issues of asynchronous control, where “asynchronous ” means the switching of the controllers has a lag to the switching of system modes. The basic asynchronous stabilization and asynchronous \(H_\infty \) control problem are both studied and the case for the system with time-varying parameter is further addressed under the modal average dwell time (MADT). Finally, the asynchronous \(H_\infty \) filter design problem is dealt with for the underlying switched linear systems with ADT switching. The phenomenon of “asynchronous” switching will unavoidably deteriorate the control performance such as the \(H_\infty \) noise attenuation index. However, it can be verified that the designed controller/filter considering the synchronous switching will be not necessarily valid in the presence of asynchronous switching. Several examples are provided to show the potential of the developed results.
Keywords
- Asynchronous Switching
- Average Dwell Time (ADT)
- Lyapunov-like Function
- Synchronous Switching
- Admissible Switching Signals
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References
Ye, H., Michel, A., Hou, L.: Stability theory for hybrid dynamical systems. IEEE Trans. Autom. Control 43(4), 461–474 (1998)
Branicky, M.: Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans. Autom. Control 43(4), 475–482 (1998)
DeCarlo, R., Branicky, M.S., Pettersson, S., Lennartson, B.: Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE 88(7), 1069–1082 (2000)
Peleties, P., DeCarlo, R.: Asymptotic stability of m-switched systems using Lyapunov functions. In: Proceedings of the 31st IEEE Conference on Decision and Control, pp. 3438–3439, Arizona, USA (1992)
Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston (2003)
Zhai, G., Ho, B., Yasuda, K., Anthony, A.: Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach. Int. J. Syst. Sci. 32(8), 1055–1061 (2001)
Zhang, L., Shi, P.: Stability, \(l_2\)-gain and asynchronous \(H_{\infty }\) control of discrete-time switched systems with average dwell time. IEEE Trans. Autom. Control 54(9), 2193–2200 (2009)
Zhang, L., Boukas, E., Shi, P.: Exponential \(H_{\infty }\) filtering for uncertain discrete-time switched linear systems with average dwell time: A \(\mu \)-dependent approach. Int. J. Robust Nonlinear Control 18(11), 1188–1207 (2008)
Xie, G., Wang, L.: Stabilization of switched linear systems with time-delay in detection of switching signal. J. Math. Anal. Appl. 305(1), 277–290 (2005)
Xie, D., Chen, X.: Observer-based switched control design for switched linear systems with time delay in detection of switching signal. IET Control Theory Appl. 2(5), 437–445 (2008)
Xie, D., Wu, Y.: Stabilisability of switched linear systems with time-varying delay in the detection of switching signal. IET Control Theory Appl. 3(4), 404–410 (2009)
Xie, D., Q, W., Wu, Y.: Average dwell-time approach to \(L_{2}\)-gain control synthesis of switched linear systems with time delay in detection of switching signal. IET Control Theory Appl. 3(6), 763–771 (2009)
Liu, H., Shen, Y.: Asynchronous finite-time stabilisation of switched systems with average dwell time. IET Control Theory Appl. 6(9), 1213–1219 (2012)
Apkarian, P., Adams, R.J.: Advanced gain-scheduling techniques for uncertain systems. IEEE Trans. Control Syst. Technol. 6(1), 21–32 (1998)
Koning, W.D.: Digital optimal reduced-order control of pulse-width modulated switched linear systems. Automatica 39(11), 1997–2003 (2003)
Sira-Ramirez, H.: Nonlinear P-I controller design for switch-mode DC-to-DC power converters. IEEE Trans. Circuits Syst.-I: Regul. Pap. 41(4), 499–513 (1991)
Tan, S.C., Bronstein, S., Nur, M., Lai, Y.M., Ioinovici, A., Tse, C.K.: Variable structure modeling and design of switched-capacitor converters. IEEE Trans. Circuits Syst.-I: Regul. Pap. 56(9), 2132–2142 (2009)
Sun, Z., Ge, S.: Switched Linear Systems: Control and Design. Springer, New York (2005)
Corona, D., Buisson, J., Schutter, B., Giua, A.: Stabilization of switched affine systems: an application to the buck-boost converter. In: Proceedings of the 2007 American Control Conference, pp. 6037–6042, New York (2007)
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Zhang, L., Zhu, Y., Shi, P., Lu, Q. (2016). Asynchronous Switched Systems: ADT Switching. In: Time-Dependent Switched Discrete-Time Linear Systems: Control and Filtering. Studies in Systems, Decision and Control, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-319-28850-5_6
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DOI: https://doi.org/10.1007/978-3-319-28850-5_6
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