Stability Theory

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.

Stability theory. - The Hurwitz Matrix and the Computation of Second-Order Information Indices. - A Summary on the Real Stability Radius and Real Perturbation Values. - The Hadamard Factorization of Hurwitz and Schur Stable Polynomials. - On the Cauchy Index of a Real Rational Function and the Index Theory of Pseudo-Lossless Rational Functions. - A Generalization of the Orlando Formula-Symbolic Manipulation Approach. - On Convex Stability Directions for Real Quasipolynomials. - From J. J. Sylvester to Adolf Hurwitz: A Historical Review. - Hurwitz Matrix for Polynomial Matrices. - Two-Dimensional Hurwitz Polynomials. - General Classes of Control-Lyapunov Functions. - Towards the Stability of Fuzzy Control Systems. - Discrete Optimization Using Analog Neural Networks with Discontinuous Dynamics. - Robust Stability. - Multiplier Theory and Operator Square Roots: Application to Robust and Time-Varying Stability. - Adaptive Control of Non-Minimum Phase Systems Subject to Unknown Bounded Disturbances. - On the Robust Stability of Time-Varying Linear Systems. - On the Computation of Stability Profiles. - Robust Stability of Family of Polynomials with 1-Norm-Bounded Parameter Uncertainties. - On the Characterization and Formation of Local Convex Directions for Hurwitz Stability. - Numerics. - Application of Quantifier Elimination to Solotareff s Approximation Problem. - Stability of Time Discretization, Hurwitz Determinants and Order Stars. - Solving Stability Problems Using Quantifier Elimination. - Stability of Numerical Methods for Solving Differential Equations. - A Fast Algorithm to Compute the Real Structured Stability Radius. - Some Open Problems. - Apendix: Original Article by A. Hurwitz A. Hurwitz. - Über die Bedingungen, unter welchen eine Gleichung nur Wurzeln mit negativen reellen Theilenbesitzt.