Quadratic stabilisation of switched affine systems

Minqing Xiao, Guisheng Zhai, Chi Huang

Research output: Contribution to journalArticle


We deal with quadratic stabilisation for switched systems which are composed of a finite set of affine subsystems, where both subsystem matrices and affine vectors in the vector fields are switched independently, and no single subsystem has desired quadratic stability. We show that if a convex combination of subsystem matrices is Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law and an output-dependent switching law such that the entire switched system is quadratically stable at the origin. If the convex combination of affine vectors is not zero, we discuss the quadratic stabilisation to a convergence set defined by the convex combination of subsystem matrices and that of affine vectors. We extend the discussion to switched uncertain affine systems with norm bounded uncertainties, and establish a quadratically stabilising state-dependent switching law based on an (Formula presented.) norm condition for a combination of subsystems. Several numerical examples show effectiveness of the results.

Original languageEnglish
JournalJournal of Control and Decision
Publication statusAccepted/In press - 2019 Jan 1



  • convergence set
  • convex combination
  • LMIs
  • norm bounded uncertainties
  • output-dependent switching
  • quadratic stabilisation
  • state-dependent switching
  • Switched affine systems (SAS)
  • switched uncertain affine systems (SUAS)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Information Systems
  • Human-Computer Interaction
  • Computer Networks and Communications
  • Control and Optimization
  • Artificial Intelligence

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