Convex directions for stable polynomials and quasipolynomials: A survey of recent results

  • L. Atanassova
  • D. Hinrichsen
  • V. L. Kharitonov
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 228)


The purpose of this chapter is to give a survey of recent results on convex directions for the sets of stable polynomials and quasipolynomials. It presents a number of analytic criteria ensuring Hurwitz and Schur stability of segments of polynomials. Convex directions are characterized in terms of root loci and it is shown that these root loci behave differently in the real and the complex case. The convex direction problem for sets of stable quasipolynomials is also discussed. Applying similar methods as in the polynomial case analytic stability criteria are obtained for segments of quasipolynomials of delay and of neutral type.


Simple Root Imaginary Axis Robust Stability Neutral Type Stable Polynomial 
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Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • L. Atanassova
    • 1
  • D. Hinrichsen
    • 1
  • V. L. Kharitonov
    • 2
  1. 1.Institut für Dynamische SystemeUniversität BremenBremenGermany
  2. 2.Control AutomaticoCINVESTAV-IPNMexico D.FMexico

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