Stability Theory

1. Front Matter

   Pages I-VII

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2. Stability theory

   1. The Hurwitz Matrix and the Computation of second-order Information Indices

      • Alessandro Beghi, Antonio Lepschy, Umberto Viaro

      Pages 1-10

   2. A Summary on the Real Stability Radius and Real Perturbation Values

      • Bo Bernhardsson, Anders Rantzer, Li Qiu

      Pages 11-18

   3. The Hadamard Factorization of Hurwitz and Schur stable Polynomials

      • J. Garloff, B. Srinivasan

      Pages 19-21

   4. On the Cauchy index of a real rational function and the index theory of pseudo-lossless rational functions

      • Yves V. Genin

      Pages 23-31

   5. A Generalization of the Orlando Formula — Symbolic Manipulation Approach

      • Henryk Górecki, Maciej Szymkat, Mieczyslaw Zaczyk

      Pages 33-42

   6. On convex stability directions for real quasipolynomials

      • L. Atanassova, D. Hinrichsen, V. L. Kharitonov

      Pages 43-52

   7. From J.J. Sylvester to Adolf Hurwitz: A Historical Review

      • Eliahu I. Jury

      Pages 53-65

   8. Hurwitz Matrix for Polynomial Matrices

      • F. J. Kraus, M. Mansour, M. Sebek

      Pages 67-74

   9. Two-dimensional Hurwitz Polynomials

      • Hari C. Reddy, P. K. Rojan, George S. Moschytz

      Pages 75-85

   10. General Classes of Control-Lyapunov Functions

       • Eduardo D. Sontag, Héctor J. Sussmann

       Pages 87-96

   11. Towards the stability of fuzzy control systems

       • Roland Strietzel

       Pages 97-106

   12. Discrete Optimization Using Analog Neural Networks with Discontinuous Dynamics

       • M. Vidyasagar

       Pages 107-112

3. Robust Stability

   1. Multiplier Theory and Operator Square Roots: Application to Robust and Time-Varying Stability

      • Brian D. O. Anderson, Soura Dasgupta

      Pages 113-124

   2. Adaptive control of non-minimum phase systems subject to unknown bounded disturbances

      • Rogelio Lozano, Dionisio A. Suárez

      Pages 125-133

   3. On the Robust Stability of Time-Varying Linear Systems

      • Mohamed Mansour, Brian D. O. Anderson

      Pages 135-149

   4. On the Computation of Stability Profiles

      • Wolfgang Sienel

      Pages 151-162

   5. Robust Stability of Family of Polynomials with 1-norm-bounded Parameter Uncertainties

      • Q.-H. Wu, M. Mansour

      Pages 163-171

   6. On the Characterization and Formation of Local Convex Directions for Hurwitz Stability

      • Ezra Zeheb

      Pages 173-180

4. Numerics

   1. Application of Quantifier Elimination to Solotareff’s Approximation Problem

      • George E. Collins

      Pages 181-190

This book contains the historical development of the seminal paper of Adolf Hurwitz, professor in mathematics at ETH (1892~1919), and its impact on other fields. The major emphasis, however, is on modern results in stability theory and its application in the theory of control and numerics. In particular, stability of the following problems is treated: linear, nonlinear and time-dependent systems, discretizations of ordinary and partial differential equations, systems with time delay on multidimensional systems. In addition robust stability, pole placement and problems related to the stability radius are treated. The book is an outgrowth of the international conference "Centennial Hurwitz on Stability Theory" which was held to honor Adolf Hurwitz, whose arti­ cle on the location of roots of a polynomial was published one hundred years ago. The conference took place at the Centro Stefano Franscini, Monte Verita, Ascona, Switzerland, on May 21~26, 1995. This book contains a collection of the papers and open problem:; discussed all that occasion. Leading researchers from allover the world working on stability theory and its application were invited to present their recent results. In one paper the historic development initiated by Hurwitz's article was discussed.

• Hadamard
• approximation
• control system
• control theory
• differential equation
• functions
• fuzzy
• index theory
• information
• minimum
• network
• neural networks
• numerical method
• numerics
• partial differential equation
• partial differential equations
• ordinary differential equations

• Seminar for Applied Mathematics, ETH Zentrum, Zürich, Switzerland

  Rolf Jeltsch

• Automatic Control Laboratory, ETH Zentrum, Zürich, Switzerland

  Mohamed Mansour

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