Strong stability of discrete-time systems

G. Halikias, L. Dritsas, A. Pantelous, V. Tsoulkas

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4 Citations (Scopus)


The paper introduces a new notion of stability for internal (state-space) autonomous system descriptions in discrete-time, referred to as strong stability which extends a parallel notion introduced in the continuous-time case. This is a stronger notion of stability compared to alternative definitions (asymptotic, Lyapunov), which prohibits systems described by natural coordinates to have overshooting responses for arbitrary initial conditions in state-space. Three finer notions of strong stability are introduced and necessary and sufficient conditions are established for each one of them. The class of discrete-time systems for which strong and asymptotic stability coincide is characterized and links between the skewness of the eigen-frame and the violation of strong stability property are obtained. Connections between the notions of strong stability in the continuous and discrete-domains are briefly discussed. Finally strong stabilization problems under state and output feedback are studied. The results of the paper are illustrated with a numerical example.

Original languageEnglish
Pages (from-to)1890-1908
Number of pages19
JournalLinear Algebra and Its Applications
Issue number7
Publication statusPublished - 1 Apr 2012
Externally publishedYes


  • Discrete-time systems
  • Eigen-frame skewness
  • Linear Matrix Inequalities (LMI's)
  • Non-overshooting response
  • Quadratic stability
  • State/output feedback
  • Strong stability

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