New Development in Quadratic L2 Performance of Switched Uncertain Stochastic Systems

Yufang Chang, Guisheng Zhai, Lianglin Xiong, Bo Fu

Research output: Contribution to journalArticlepeer-review


Global quadratic stability and L2 performance in probability (quadratic stability and L2 gain γ in probability: abbreviated as GQL2 (γ)-P) is studied for switched systems consisting of linear stochastic subsystems with norm-bounded uncertainties. Under the assumption that there is no single subsystem achieving GQL2 (γ)-P, it is shown that if there exists a convex combination of subsystems achieving GQL2 (γ)-P, then a state-dependent switching law, based on the convex combination of subsystems, is proposed under which the switched system achieves GQL2 (γ)-P. Then, the discussion is extended to the case involving state feedback controller gain. A numerical example and the application to DC–DC boost converters are provided to demonstrate the proposed design condition and the algorithm.

Original languageEnglish
Article number1963
JournalElectronics (Switzerland)
Issue number13
Publication statusPublished - 2022 Jul 1


  • convex combination
  • global quadratic L performance γ in probability (GQL (γ)-P)
  • linear matrix inequalities (LMIs)
  • norm-bounded uncertainties
  • state-dependent switching laws
  • switched uncertain stochastic systems (SUSS)

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Hardware and Architecture
  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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