## Stability Theory: Hurwitz Centenary Conference. Centro Stefano Franscini, Ascona, 1995Rolf Jeltsch, Mohamed Mansour 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. |

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### Contents

The Hurwitz Matrix and the Computation of secondorder Information Indices | 1 |

A Summary on the Real Stability Radius and Real Perturbation Values | 11 |

The Hadamard Factorization of Hurwitz and Schur stable Polynomials | 19 |

On the Cauchy index of a real rational function and the index theory of pseudolossless rational functions | 23 |

A Generalization of the Orlando Formula Symbolic Manipulation Approach | 33 |

On convex stability directions for real quasipolynomials | 43 |

A Historical Review | 53 |

Hurwitz Matrix for Polynomial Matrices | 67 |

Adaptive control of nonminimum phase systems subject to unknown bounded disturbances | 125 |

On the Robust Stability of TimeVarying Linear Systems | 135 |

On the Computation of Stability Profiles | 151 |

Robust Stability of Family of Polynomials with 1normbounded Parameter Uncertainties | 163 |

On the Characterization and Formation of Local Convex Directions for Hurwitz Stability | 173 |

Application of Quantifier Elimination to Solotareffs Approximation Problem | 181 |

Stability of Time Discretization Hurwitz Determinants and Order Stars | 191 |

Solving Stability Problems Using Quantifier Elimination | 205 |

Twodimensional Hurwitz Polynomials | 75 |

General Classes of ControlLyapunov Functions | 87 |

Towards the stability of fuzzy control systems | 97 |

Discrete Optimization Using Analog Neural Networks with Discontinuous Dynamics | 107 |

Application to Robust and TimeVarying Stability | 113 |

Stability of Numerical Methods for solving Differential Equations | 211 |

A Fast Algorithm to Compute the Real Structured Stability Radius | 219 |

Open Problems | 231 |

Über die Bedingungen unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilen besitzt | 239 |

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Stability Theory: Hurwitz Centenary Conference Centro Stefano Franscini ... Rolf Jeltsch,Mohamed Mansour No preview available - 2011 |

### Common terms and phrases

adaptive control algebraic algorithm analysis application approximation asymptotic asymptotically stable B.D.O. Anderson bounded Cauchy index characteristic polynomial coefficients complex computation construction continuous functions control systems converge convex combination convex direction defined denote derivative differential equations discrete dynamics eigenvalues equivalent exists factors finite formula fuzzy controller fuzzy unit given Hence Hurwitz determinants Hurwitz matrix Hurwitz polynomials Hurwitz stability Hurwitz stable IEEE IEEE Trans imaginary axis input interval ISNM Jeltsch Lemma Lyapunov equation Lyapunov function Mathematics method neural network nonlinear obtained operator optimization order star paper PI(s positive real proof pseudo-lossless functions qepcad quantifier elimination quasipolynomials rational function real polynomials robust stability roots Routh scheme Section solution solve stability conditions stability profile stability radius stable polynomials strict Hurwitz polynomial sufficient condition symmetric Theorem theory transfer function uncertain parameters value set variables vector zero

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