Mixed ℓ₁/ℓ_ Fault Detection for Positive 2-D Systems With Distributed Delays

Zhaoxia Duan, Jinna Fu, Choon Ki Ahn, Zhengrong Xiang, Imran Ghous

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


This work discusses the fault detection problem for two-dimensional (2-D) positive systems (PSs) with distributed delays. First, a systematic method is proposed for the computation of exact values of ℓ₁-gain and ℓ_- index for delay-free systems, and the dimension expansion technique is used to transfer the computation of ℓ₁/ℓ_ index for 2-D delayed PSs to one of the delay-free systems. Second, necessary and sufficient conditions are established such that the 2-D delayed PSs are asymptotically stable with a desired ℓ₁/ℓ_ performance level (PL) ɣ/β. Third, based on the above results, some NCSs are established such that the disturbance and the fault impact on the output signal are minimized and maximized, respectively. An algorithm (iterative) is formulated for the solution of the convex optimization problem. Finally, the potency and accuracy of the developed theoretical results are exhibited by an example.

Original languageEnglish
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Publication statusAccepted/In press - 2022


  • ℓ₁/ℓ_ index
  • Delays
  • Fault detection
  • Fault detection (FD)
  • Indexes
  • multiple delays
  • observer
  • Observers
  • Process control
  • Stability criteria
  • Two dimensional displays

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


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