Multivariable extension of the Tsypkin criterion using a lyapunov function approach

Vikram Kapila, Wassim M. Haddad

Research output: Contribution to journalConference articlepeer-review


For analyzing the stability of discrete-time systems containing a feedback nonlinearity the Tsypkin criterion is the closet analog to the Popov criterion which is used for analyzing such systems in continuous-time. Traditionally the proof of this criterion is based upon input-output properties and function analytic methods. In this paper we extend the Tsypkin criterion to multivariable systems containing an arbitrary number of monotonic sector-bounded memoryless time-invariant nonlinearities, along with providing a Lyapunov function proof for this classical result.

Original languageEnglish (US)
Pages (from-to)843-844
Number of pages2
JournalProceedings of the IEEE Conference on Decision and Control
StatePublished - 1994
EventProceedings of the 33rd IEEE Conference on Decision and Control. Part 1 (of 4) - Lake Buena Vista, FL, USA
Duration: Dec 14 1994Dec 16 1994

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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