Abstract
In this chapter, the issue of performance analysis for the time-dependent switched systems with several typical switching signals will be studied. We will first focus our attention on the switched systems with \(l_{2}\) disturbances and present the results of weighted/non-weighted \(l_{2}\)-gain analyses for the switching signals subject to arbitrary switching, ADT switching, and PDT switching, respectively. Then, considering the switching signals are to have MPDT property, we will give the tube-based robustness analysis for switched systems with \(l_{\infty }\) disturbances with the aid of set-theoretic method. Finally, one example is given to verify the effectiveness of developed results on the section of tube-based robustness analysis for discrete-time switched systems with MPDT switching; the verifications of the results corresponding to other switching signals will be illustrated in later chapters coping with \(H_{\infty }\) control or filtering.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Daafouz, J., Riedinger, P., Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. Autom. Control 47(11), 1883–1887 (2002)
Jin, S.H., Park, J.B.: Robust \(H_{\infty }\) filter for polytopic uncertain systems via convex optimization. IEE Proc. Part D: Control Theory Appl. 2001 148(1), 55–59 (2001)
Sun, X., Zhao, J., Hill, D.: Stability and \(L_{2}\)-gain analysis for switched delay systems: a delay-dependent method. Automatica 42(10), 1769–1774 (2006)
Zhai, G., Ho, B., Yasuda, K., Michel, A.: Disturbance attenuation properties of time-controlled switched systems. J. Frankl. Inst. 338(7), 765–779 (2001)
Zhao, J., Hill, D.: On stability, \(L_{2}\)-gain and \(H_{\infty }\) control for switched systems. Automatica 44(5), 1220–1232 (2008)
Zhang, L., Wang, C., Chen, L.: Stability and stabilization of a class of multimode linear discrete-time systems with polytopic uncertainties. IEEE Trans. Ind. Electron. 56(9), 3684–3692 (2009)
Wang, D., Wang, W., Shi, P.: Exponential \(H_{\infty }\) filtering for switched linear systems with interval time-varying delay. Int. J. Robust Nonlinear Control 19(5), 532–551 (2009)
Colaneri, P., Bolzern, P., Geromel, J.C.: Root mean square gain of discrete-time switched linear systems under dwell time constraints. Automatica 47(8), 1677–1684 (2011)
Lin, H., Antsaklis, P.J.: Hybrid state feedback stabilization with \(l_{2}\) performance for discrete-time switched linear systems. Int. J. Control 81(7), 1114–1124 (2008)
Hespanha, J., Morse, A.: \(\mathit{L}_{2}\)-induced gains of switched linear systems. In: Blondel, V.D., Sontag, E.D., Vidyasagar, M., Willenms, J.C. (eds.). Springer, London (1999)
Liberzon, D.: Switching in Systems and Control. Birkhauser, Boston, MA (2003)
Feron, E., Gahinet, P.: Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions. IEEE Trans. Autom. Control 41(7), 1041–1046 (1996)
Hespanha, J.P.: Root-mean-square gains of switched linear systems. IEEE Trans. Autom. Control 48(11), 2040–2045 (2003)
Hespanha, J.: Uniform stability of switched linear systems: Extensions of LaSalle’s invariance principle. IEEE Trans. Autom. Control 49(4), 470–482 (2004)
Rawlings, J., Mayne, D.: Model Predictive Control: Theory and Design. Nob Hill Press, Madison (2009)
Dehghan, M., Ong, C.: Characterization and computation of disturbance invariant sets for constrained switched linear systems with dwell time restriction. Automatica 48(9), 2175–2181 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Zhang, L., Zhu, Y., Shi, P., Lu, Q. (2016). Performance Analysis. 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_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-28850-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28849-9
Online ISBN: 978-3-319-28850-5
eBook Packages: EngineeringEngineering (R0)