Reduced linear fractional representation of nonlinear systems for stability analysis

Péter Polcz, Tamás Péni, G. Szederkényi

Research output: Contribution to journalArticle

2 Citations (Scopus)


Based on symbolic and numeric manipulations, a model simplification technique is proposed in this paper for the linear fractional representation (LFR) and for the differential algebraic representation introduced by Trofino and Dezuo (2013). This representation is needed for computational Lyapunov stability analysis of uncertain rational nonlinear systems. The structure of the parameterized rational Lyapunov function is generated from the linear fractional representation (LFR) of the system model. The developed method is briefly compared to the n-D order reduction technique known from the literature. The proposed model transformations does not affect the structure of Lyapunov function candidate, preserves the well-posedness of the LFR and guarantees that the resulting uncertainty block is at most the same dimensional as the initial one. The applicability of the proposed method is illustrated on two examples.

Original languageEnglish
Pages (from-to)37-42
Number of pages6
Issue number2
Publication statusPublished - Jan 1 2018



  • computational methods
  • Linear fractional representation
  • Lyapunov functions
  • model simplification
  • stability analysis

ASJC Scopus subject areas

  • Control and Systems Engineering

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