A Simplified Approach to Analyze Complementary Sensitivity Trade-offs in Continuous-Time and Discrete-Time Systems

Neng Wan, Dapeng Li, Naira Hovakimyan

Research output: Contribution to journalArticle


Continuous-time and discrete-time complementary sensitivity Bode integrals (CSBIs) are investigated via a simplified approach in this note. For continuous-time feedback systems with unbounded frequency domain, the CSBI weighted by <formula><tex>$1/\omega^2$</tex></formula> is considered, where this simplified method reveals a more explicit relationship between the value of CSBI and the structure of the open-loop transfer function. With a minor modification of this method, the CSBI of discrete-time system is derived, and illustrative examples are provided. Compared with the existing results on CSBI, neither Cauchy integral theorem nor Poisson integral formula is used throughout the analysis, and the analytic constraint on the integrand is removed.

Original languageEnglish (US)
JournalIEEE Transactions on Automatic Control
StatePublished - Jan 1 2019



  • Complementary sensitivity Bode integral
  • Discrete-time systems
  • Frequency-domain analysis
  • Harmonic analysis
  • Measurement uncertainty
  • Poles and zeros
  • Sensitivity
  • control trade-offs
  • linear systems
  • simplified approach

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this