Abstract
In this chapter, the issue of stability and \(\ell _{2}\)-gain analysis for discrete-time switched systems is addressed with MDPDT switching. Compared with the MDADT switching signal, the MDPDT switching signal is more general and flexible since it can cover MDADT switching as a special case. Under the MDPDT switching, the achieved disturbance attenuation performance is non-weighted, which is more flexible in practice than the weighted one. Moreover, the QTD technique is adopted to obtain less conservative criteria. First of all, the stability and \(\ell _{2}\)-gain criteria are presented for general discrete-time switched systems. On this basis, LMI conditions to guarantee the stability and \(\ell _{2}\)-gain performance are deduced for discrete-time switched linear systems with uncertainties. Finally, numerical examples are provided to illustrate the effectiveness of the developed criteria.
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References
Han, T., Ge, S.S., Lee, T.H.: Persistent dwell-time switched nonlinear systems: variation paradigm and gauge design. IEEE Trans. Autom. Control 55(2), 321–337 (2010)
Hespanha, J.P.: Root-mean-square gains of switched linear systems. IEEE Trans. Autom. Control 48(11), 2040–2045 (2003)
Hespanha, J.P.: Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle. IEEE Trans. Autom. Control 49(4), 470–482 (2004)
Zhang, L., Zhuang, S., Shi, P.: Non-weighted quasi-time-dependent \(\mathscr {H}_{\infty }\) filtering for switched linear systems with persistent dwell-time. Automatica 54, 201–209 (2015)
Zhang, L., Zhuang, S., Shi, P., Zhu, Y.: Uniform tube based stabilization of switched linear systems with mode-dependent persistent dwell-time. IEEE Trans. Autom. Control 60(11), 2994–2999 (2015)
Zhong, G., Yang, G.: Simultaneous control and fault detection for discrete-time switched delay systems under the improved persistent dwell time switching. IET Control Theory Appl. 10(7), 814–824 (2016)
Zhou, K., Khargonekar, P.P.: Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Syst. Control Lett. 10(1), 17–20 (1988)
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Fei, Z., Shi, S., Shi, P. (2020). Stability and \(\ell _{2}\)-Gain Analysis. In: Analysis and Synthesis for Discrete-Time Switched Systems. Studies in Systems, Decision and Control, vol 244. Springer, Cham. https://doi.org/10.1007/978-3-030-25812-2_9
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DOI: https://doi.org/10.1007/978-3-030-25812-2_9
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