Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities

Akn Delibaşi, Didier Henrion

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bézoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour of PENNON.

Original languageEnglish
Pages (from-to)2494-2505
Number of pages12
JournalInternational Journal of Control
Issue number12
Early online date13 Dec 2010
Publication statusPublished - Dec 2010
Externally publishedYes


  • Hermite stability criterion
  • nonlinear semidefinite programming
  • polynomial matrix inequality
  • static output feedback

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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