Robust State-Feedback Synthesis for LTI Systems

  • Yoshio EbiharaEmail author
  • Dimitri Peaucelle
  • Denis Arzelier
Part of the Communications and Control Engineering book series (CCE)


In this chapter, the SV-LMIs of Chap.  2 are reconsidered for robust state-feedback synthesis. The results rely on the structuring of the S-variables. An interpretation in terms of virtual stable model is given to this structure. Moreover, we show the effect of this structuring on conservatism reduction. It happens to be of different nature in the discrete-time and continuous-time cases.


State Feedback Gain Continuous-time Case Conservative Reduction Quadratic Stability State Feedback Controller Synthesis 
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  1. 1.
    Bernussou J, Geromel JC, Peres PLD (1989) A linear programing oriented procedure for quadratic stabilization of uncertain systems. Syst Control Lett 13:65–72Google Scholar
  2. 2.
    de Oliveira MC, Bernussou J, Geromel JC (1999) A new discrete-time stability condition. Syst Control Lett 37(4):261–265Google Scholar
  3. 3.
    de Oliveira MC, Geromel JC, Hsu L (1999) LMI characterization of structural and robust stability: the discrete-time case. Linear Algebra Appl 296(1–3):27–38Google Scholar
  4. 4.
    Chilali M, Gahinet P (1996) \(H_\infty \) design with pole placement constraints: an LMI approach. IEEE Trans Automat Control 41:358–367MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Chilali M, Gahinet P, Apkarian P (December 1999) Robust pole placement in LMI regions. IEEE Trans Automat Control 44(12):2257–2270Google Scholar
  6. 6.
    Ashokkumar CR, Yedavalli RK (1997) Eigenstructure preturbation analysis in disjointed domains for linear uncertain systems. Int J Control 67:887–899MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bachelier O, Henrion D, Pradin B, Mehdi D (2004) Root-clustering of a matrix in intersections or unions of regions. Siam J Control Optimization 43(3):1078–1093MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Rejichi O, Bachelier O, Chaabane M, Mehdi D (2008) Robust root clustering analysis in a union of subregions for descriptor systems. In: IEE Proceedings of Control Theory and applicationsGoogle Scholar
  9. 9.
    Scherer CW, Gahinet P, Chilali M (1997) Multiobjective output-feedback control via LMI optimization. IEEE Trans Autom Control 42(7):896–911MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Shcherbakov P, Dabbene F (2011) On the generation of random stable polynomials. European Journal of Control 17(2):145–159Google Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Yoshio Ebihara
    • 1
    Email author
  • Dimitri Peaucelle
    • 2
  • Denis Arzelier
    • 2
  1. 1.Department of Electrical EngineeringKyoto UniversityKyotoJapan
  2. 2.Laboratory for Analysis and Architecture of Systems ScienceNational Centre for Scientific ResearchToulouseFrance

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