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

By Edmond A. Jonckheere

During this publication, likely unrelated fields -- algebraic topology and powerful regulate -- are introduced jointly. The ebook develops algebraic/differential topology from an application-oriented viewpoint. The publication takes the reader on a course ranging from a well-motivated strong balance challenge, displaying 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 concerns akin 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 rationalization of the shortcoming of continuity of the soundness margin relative to rounding mistakes. The publication is acceptable for graduate scholars in engineering and/or utilized arithmetic, educational researchers and governmental laboratories.

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Extra resources for Algebraic and Differential Topology of Robust Stability

Sample text

206 ; the vertical axis is 154 FIGURES Fig. 2 xxxvii Semisimplicial version of the principal bundle of the Mobius strip. Thick lines and dark vertices correspond to the vertex f° of the fiber complex; thin lines and circled vertices correspond to vertex fl of fiber complex F {f0,f1}. 220 Fig. 3 Illustration of lack of fibration property of the orthogonal projection of a circle on a line. 225 Fig. 1 The fundamental or Poincare group of the template of an open-loop unstable system. 260 Fig. 1 Image of 2 under Nyquist map.

Fig. 19 Critical value curves drawn in the supertemplate for a = 1 (Example II). 3. Fig. 20 Images of the sample points of a uniform gridding of the domain of uncertainty [0, 2 ]2 of Example II. 19. 3. 438 441 442 442 443 443 444 445 446 447 Fig. 1 Stratification of Kharitonov cube. 452 Fig. 1 Fig. 2 A tubular neighborhood. The isotopy from the nominal to the perturbed crossover. 487 485 Fig. 3 Crossover X region and its projection on the space of uncertain parameters. Fig. 4 The largest square that can be inserted within the stable region for a < a ; the numbers indicate the number of LHP closed-loop poles.

Fig. 3 (Example II). Observe that the swallow tail is shrinking. Fig. 16 Plot of critical values of f versus 9 for a = 2 (Example II). Observe that the swallow tail has disappeared. Fig. 17 The part of the boundary of the supertemplate for a = 1 (Example II), obtained as image of critical point curves of Morse index = 0, 2. Observe the "kink" across the real axis. Fig. 18 The part of the boundary of the supertemplate for a = 2 (Example II), obtained as image of critical point curves of Morse index A = 0, 2.

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