Algebraic and Differential Topology of Robust Stability by Edmond A. Jonckheere

By Edmond A. Jonckheere

During this publication, doubtless unrelated fields -- algebraic topology and powerful keep watch over -- are introduced jointly. The booklet develops algebraic/differential topology from an application-oriented perspective. The booklet takes the reader on a direction ranging from a well-motivated strong balance challenge, exhibiting the relevance of the simplicial approximation theorem and the way it may be successfully carried out utilizing computational geometry. The simplicial approximation theorem serves as a primer to extra severe topological matters equivalent to the obstruction to extending the Nyquist map, K-theory of sturdy stabilization, and at last the differential topology of the Nyquist map, culminating within the clarification of the inability of continuity of the soundness margin relative to rounding mistakes. The ebook is appropriate for graduate scholars in engineering and/or utilized arithmetic, educational researchers and governmental laboratories.

Show description

Read Online or Download Algebraic and Differential Topology of Robust Stability PDF

Similar robotics & automation books

Advanced Control Engineering

Complex keep watch over Engineering offers a whole direction up to speed engineering for undergraduates of all technical disciplines. beginning with a simple review of hassle-free regulate thought this article speedy strikes directly to a rigorous exam of extra complicated and leading edge date facets equivalent to strong and clever keep watch over, together with neural networks and genetic algorithms.

Stellgeräte für die Prozeßautomatisierung: Berechnung — Spezifikation — Auswahl

Das Buch behandelt sowohl die theoretischen Grundlagen im Zusammenhang mit Stellgeräten, als auch die zahlreichen Bauformen und Ausführungsvarianten der Regelventile, Stellantriebe und Hilfsgeräte. Im Mittelpunkt steht die Anwendung dieser Geräte bei der Prozeßautomatisierung.

Hybrid Predictive Control for Dynamic Transport Problems

Hybrid Predictive keep an eye on for Dynamic delivery difficulties develops equipment for the layout of predictive keep watch over thoughts for nonlinear-dynamic hybrid discrete-/continuous-variable structures. The method is designed for real-time purposes, quite the research of dynamic delivery structures. Operational and repair rules are thought of, in addition to expense aid.

Extra resources for Algebraic and Differential Topology of Robust Stability

Sample text

It follows that there could be a discrepancy between the zeros of det(D + N) and the poles of (D + N ) - l ; to be more specific, ROBUST MULTIVARIABLE NYQUIST CRITERION 9 However, if any cancellation occurs, this could only be a LHP pole/zero cancellation because the bi(s)'s are Hurwitz. Therefore, { RHP poles of (D+N)-1} = { RHP zeros of det (D+N)} At this stage we have reached the following result: The multivariable closed-loop matrix (/ + L 0)-1L 0 is stable iff det(D(s) + N(s)) has no right half-plane zeros.

1 Nyquist mapping formulation of Kharitonov's theorem. 27 Fig. 2 Example of a Schwarz-Christoffel conformal mapping exhibiting some pathological boundary behavior. 39 Fig. 3 A domain with a boundary that is not locally connected. 40 Fig. 1 The standard 2-simplex. 63 Fig. 2 Simplicial cylinder. 64 Fig. 3 Simplicial 2-torus. 64 Fig. 4 The simplicial Mobius strip. 65 Fig. 5 Illustration of the nerve of a covering. 67 Fig. 6 The barycentric and Q-subdivisions of the simplex. 69 Fig. 7 The stellar subdivision of the simplex.

An injective group homornorphism will sometimes be called a monomorphism. e to suggest that algebraic topology has now reached a sufficient degree of maturity so that it should be regarded as a tool available for use in appropriate branches of analysis. At least I hope it will be the natural thing for a mathematician to ask: if I vary the coefficients or parameters of my problem, what sort of a topological space do I get—is it for example contractible and if not, what is the significance of its topological invariants?

Download PDF sample

Rated 4.15 of 5 – based on 33 votes