A brief look at the Tsypkin criterion: from analysis to design

Tsypkin was among the first to recognize the importance of the Popov criterion and to extend it to discrete-time systems in the form now known as the Tsypkin criterion. This paper briefly reviews the evolution of the Tsypkin criterion from its original use in absolute stability analysis to its current application as a design tool. Copyright © 2001 John Wiley & Sons, Ltd.

[1]  Ya. Z. Tsypkin,et al.  A Criterion for Absolute Stability of Automatic Pulse Systems with Monotonic Characteristics of the Nonlinear Element , 1964 .

[2]  E. Jury,et al.  Discrete-time positive-real lemma revisited: the discrete-time counterpart of the Kalman-Yakubovitch lemma , 1994 .

[3]  Michael P. Polis,et al.  Robust Stabilization and Robust Performance Using Model Reference Control and Modeling Error Compensation , 1991, 1991 American Control Conference.

[4]  Wassim M. Haddad,et al.  A multivariable extension of the Tsypkin criterion using a Lyapunov-function approach , 1996, IEEE Trans. Autom. Control..

[5]  E. I. Jury,et al.  On the stability of a certain class of nonlinear sampled-data systems , 1964 .

[6]  T. Sharma,et al.  On the absolute stability of multivariable discrete-time nonlinear systems , 1981 .

[7]  Brian D. O. Anderson,et al.  Discrete positive-real fu nctions and their applications to system stability , 1969 .

[8]  Bruce A. Francis,et al.  Optimal Sampled-Data Control Systems , 1996, Communications and Control Engineering Series.

[9]  Sang Woo Kim,et al.  A Revisited Tsypkin Criterion for Discrete-Time Nonlinear Lur'e Systems with Monotonic Sector-Restrictions , 1998, Autom..

[10]  P. Khargonekar,et al.  Solution to the positive real control problem for linear time-invariant systems , 1994, IEEE Trans. Autom. Control..

[11]  Kamal Premaratne,et al.  Some corrections on "Discrete-time positive-real lemma revisited: the discrete-time counterpart of the Kalman-Yakubovitch lemma" , 1996 .

[12]  G. P. Szegö,et al.  ON THE ABSOLUTE STABILITY OF SAMPLED-DATA CONTROL SYSTEMS. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Petros A. Ioannou,et al.  Design of strictly positive real systems using constant output feedback , 1999, IEEE Trans. Autom. Control..

[14]  D. Siljak,et al.  Polytopes of Nonnegative Polynomials , 1989, 1989 American Control Conference.

[15]  A. K. Mahalanabis,et al.  On the stability of discrete non-linear feedback systems with state-dependent noise , 1975 .

[16]  P. Dubock.  Erratum: Numerical analysis of forward and reverse bias potential distribution in a 2-dimensional p-n junction with applications to capacitance calculations , 1969 .

[17]  R. Kálmán.  LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. G. Safonov,et al.  Synthesis of positive real feedback systems: a simple derivation via Parrott's theorem , 1997, IEEE Trans. Autom. Control..

[19]  G. Zames.  On the input-output stability of time-varying nonlinear feedback systems Part one: Conditions derived using concepts of loop gain, conicity, and positivity , 1966 .

[20]  D. Siljak.  Algebraic criteria for positive realness relative to the unit circle , 1973 .