Brief Paper: A Revisited Tsypkin Criterion for Discrete-Time Nonlinear Lur'e Systems with Monotonic Sector-Restrictions

  • Authors:

  • POOGYEON PARK;SANG WOO KIM

  • Affiliations:

  • Department of Electronics and Electrical Engineering, Pohang University of Science and Technology, Kyung-buk, 790-784, South Korea.;Department of Electronics and Electrical Engineering, Pohang University of Science and Technology, Kyung-buk, 790-784, South Korea.

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 1998

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Abstract

This paper revisits a well-known Tsypkin criterion for stability analysis of discrete-time nonlinear LurÕe systems. When nonlinearities are monotonic and sector restricted by [0, *1 ], where *1 is positive deÞnite, it is shown by Kapila and Haddad that the system is absolutely stable if a function G 0 (z)"*1 ~1#MI#(1!z~1)K`NG(z) is strictly positive real, whereK` is nonnegative diagonal and G(z) represents a transfer function of the linear part of the LurÕe system with invertible or identically zero G(0). This paper extends this criterion when *1 is positive diagonal, by choosing a new Lyapunov function to obtain an LMI criterion. From a frequency-domain interpretation of this LMI criterion, another su¦cient criterion is generated which establishes that the system is absolutely stable if a function G 0 (z)"*1 ~1#MI#(1!z~1)K`#(1!z)K~N G(z) is strictly positive real, whereK` andK~ are nonnegative diagonal and orthogonal to each other.(1998 Elsevier Science Ltd. All rights reserved