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Ultimate Bounds and Robust Invariant Sets for Linear Systems with State-Dependent Disturbances

  • Sorin OlaruEmail author
  • Vasso Reppa
Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 464)

Abstract

The objective of this chapter is to present a methodology for computing robust positively invariant sets for linear, discrete time-invariant systems that are affected by additive disturbances, with the particularity that these disturbances are subject to state-dependent bounds. The proposed methodology requires less restrictive assumptions compared to similar established techniques, while it provides the framework for determining the state-dependent (parameterized) ultimate bounds for several classes of disturbances. The added value of the proposed approach is illustrated by an optimization-based problem for detecting the mode of functioning of a switching system.

Keywords

Invariant sets Ultimate bounds State dependent disturbances 

Notes

Acknowledgments

The results presented in this chapter were initiated in the framework of the French-Italian collaborative research project Galileo 2014. The authors would like to thank Prof. F. Blanchini, Prof. D. Casagrane, Prof. S. Miani, and G. Giordano for the fruitful discussion on the topic. This work was supported by the People Programme (Marie Curie Actions) of the European FP7 (2007–2013) under REA grant agreement n\(^{\circ }\) 626891 (FUTuRISM).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Laboratory of Signals and Systems (UMR CNRS 8506)CentraleSupélec-CNRS-Univ. Paris-Sud, Université Paris-SaclayGif-sur-YvetteFrance

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