By Anthony J. Pritchard (auth.), Fritz Colonius, Uwe Helmke, Dieter Prätzel-Wolters, Fabian Wirth (eds.)

ISBN-10: 1461201799

ISBN-13: 9781461201793

ISBN-10: 1461266491

ISBN-13: 9781461266495

"This quantity comprises lectures offered on the workshop ‘Advances in Mathematical structures Theory’…. the various members are top foreign researchers within the box. the most subject matters are fresh advances in nonlinear structures conception, together with parameterization difficulties and behavior of the linear procedure, convolution codes, complementary and hybrid structures. Controllability and stabilizability of infinite-dimensional platforms are taken care of as well." —Applications of Mathematics

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Rantzer, Stability conditions for polytopes of polynomials, IEEE Trans. Auto. Control 37:79--89, 1992. B. Paice Fabian R. Wirth! ABSTRACT In this chapter we consider the problem of analyzing the robustness of stability of nonlinear systems with respect to time-varying perturbations. We show that generically the stability radii of a singular fixed point of the nonlinear system and that of the corresponding linearization coincide. A brief introduction to a method for the calculation of the linear stability radius is presented.

2, Ilx(t)11 ::s: Mllxoll, t ~ O. References [I] K. M. Butler and B. F. Farrell, Three dimensional optimal perturbations in viscous shear flow, Phys. Fluids A 4:1637-1650, 1992. [2] E. Gallestey, D. Hinrichsen, and A. J. Pritchard, Spectral value sets of closed linear operators, Pmc. Royal Soc. London A 456:1397-1418, 2000. [3] S. K. Godunov, Spectral portraits of matrices and criteria of spectrum dichotomy, Pmc. Int. Conference on Computer Arithmetic, Scientific Computation and Mathematical Modelling.

Suppose that][{n is a Hilbert space with inner product ( . , p. ) is the usual Euclidean inner product. Then the adjoint of A, A" = P-1AT P, where AT is the complex conjugate and transpose of A. So A generates a contraction semigroup on][{n if and only if We see therefore that any matrix A with u(A) C C_ generates a contraction semigroup with respect to some norm induced by a particular inner product. The property of generating a contraction semigroup is robust. To see this let ::Ne be the set of all n x n matrices that do not generate a contraction semigroup.

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Advances in Mathematical Systems Theory: A Volume in Honor of Diederich Hinrichsen by Anthony J. Pritchard (auth.), Fritz Colonius, Uwe Helmke, Dieter Prätzel-Wolters, Fabian Wirth (eds.)


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