Abstract
Chapter 7 is dedicated to the analysis of discrete-time periodic systems by means of SV-LMIs. For that special case the SV-LMIs have interesting non-causal system interpretations. Similarly to the LTI case, SV-LMIs are effective for reducing the conservatism of the analysis results when dealing with discrete-time periodic systems affected by polytopic uncertainties.
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References
Bittanti S, Colaneri P (1996) Analysis of discrete-time linear periodic systems. In: Leondes CT (ed) Control and dynamic systems. Academic Press, New York, pp 313–339
Bittanti S, Bolzern P, Colaneri P (1985) The extended periodic Lyapunov lemma. Automatica 21:603–605
De Souza CE, Trofino A (2000) An LMI approach to stabilization of linear discrete-time periodic systems. Int J Control 73:696–709
Ebihara Y, Peaucelle D, Arzelier D (2010) Analysis of uncertain discrete-time linear periodic systems based on system lifting and LMIs. Eur J Control 16(5):532–544
Bittanti S, Colaneri P (2009) Periodic systems: filtering and control. Springer, London
Zhang C, Zhang J, Furuta K (1997) Analysis of \(H_2\) and \(H_\infty \) performance of discrete periodically time-varying controllers. Automatica 33(4):619–634
Farges C, Peaucelle D, Arzelier D, Daafouz J (2007) Robust \(H_2\) performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. Syst Control Lett 56:159–166
Ebihara Y, Peaucelle D, Arzelier D (2008) Periodically time-varying dynamical controller synthesis for polytopic-type uncertain discrete-time linear systems. In: Proceedings of the conference on decision and control, pp 5438–5443
Ebihara Y (2013) Periodically time-varying memory state-feedback for robust \(H_2\) control of uncertain discrete-time linear systems. Asian J Control 15(2):409–419
Sturm JF (1999) Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim Methods Softw 11–12:625–653
Löfberg J (2004) YALMIP: a toolbox for modeling and optimization in MATLAB. In: Proceedings of the IEEE computer aided control system design, pp 284–289
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Ebihara, Y., Peaucelle, D., Arzelier, D. (2015). Robust Performance Analysis of Discrete-Time Periodic Systems. In: S-Variable Approach to LMI-Based Robust Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-6606-1_7
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DOI: https://doi.org/10.1007/978-1-4471-6606-1_7
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