Using an Observer to Transform Linear Systems into Strictly Positive Real Systems

J. Collado, R. Lozano, Rolf Johansson

Research output: Contribution to journalArticlepeer-review

Abstract

In this note, we study the extension of the class of linear time invariant plants that may be transformed into SPR systems introducing an observer. It is shown that for open loop stable systems a cascaded observer achieves the result. For open loop unstable systems an observer-based feedback is required to succeed. In general any stabilizable and observable system may be transformed into an SPR system defining a new output based on the observer state. This overcomes the old conditions of minimum phase and relative degree one for the case of keeping the original output. The result is illustrated with some examples.
Original languageEnglish
Pages (from-to)1082-1088
JournalIEEE Transactions on Automatic Control
Volume52
Issue number6
DOIs
Publication statusPublished - 2007

Subject classification (UKÄ)

  • Control Engineering

Free keywords

  • strictly positive realness (SPR)
  • passivity
  • observers
  • Kalman-Yakubovich-Popov (KYP) lemma
  • Lyapunov functions
  • strictly positive realness
  • (SPR) systems

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