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By Andrew Lewis

ISBN-10: 3319086375

ISBN-13: 9783319086378

ISBN-10: 3319086383

ISBN-13: 9783319086385

This short offers an outline of a brand new modelling framework for nonlinear/geometric keep an eye on concept. The framework is meant to be—and proven to be—feedback-invariant. As such, Tautological keep an eye on platforms presents a platform for knowing primary structural difficulties in geometric regulate idea. a part of the newness of the textual content stems from the range of regularity periods, e.g., Lipschitz, finitely differentiable, soft, actual analytic, with which it offers in a accomplished and unified demeanour. The therapy of the real genuine analytic category in particular displays fresh paintings on actual analytic topologies by way of the writer. utilized mathematicians drawn to nonlinear and geometric keep an eye on idea will locate this short of curiosity as a kick off point for paintings within which suggestions invariance is necessary. Graduate scholars operating up to speed concept can also locate Tautological regulate platforms to be a stimulating place to begin for his or her research.

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J Math Soc Jpn 18:398–404 48. Nijmeijer H (1983) Nonlinear multivariable control: a differential geometric approach. D. thesis, University of Groningen 49. Nijmeijer H, van der Schaft AJ (1982) Controlled invariance for nonlinear systems. Institute of Electrical and Electronics Engineers. Trans Autom Control 27(4):904–914 50. Nijmeijer H, van der Schaft AJ (1990) Nonlinear dynamical control systems. Springer, Berlin 51. Pasillas-Lépine W, Respondek W (2002) Contact systems and corank one involutive subdistributions.

M+lip The family of seminorms p K , K ⊆ M compact, defines a locally convex topology for Γ m+lip (E), which we call the Cm+lip -topology, having the following attributes: 1. , it is a Fréchet topology; 2. it is separable; 3. it is characterised by the sequences converging to zero, which are the sequences (ξ j ) j→Z>0 such that, for each K ⊆ M, the sequence ( jm ξ j |K ) j→Z>0 converges m uniformly to zero in both seminorms λm K and p K ; m+lip is a norm that gives the Cm+lip -topology. 4. 5] for details.

Gardner RB (1989) The method of equivalence and its applications. No. 58 in Regional Conference Series in Applied Mathematics. Society for Industrial and Applied Mathematics, Philadelphia, PA 20. Godement R (1958) Topologie algébrique et théorie des faisceaux. No. 13 in Publications de l’Institut de mathématique de l’Université de Strasbourg. Hermann, Paris 21. Groethendieck A (1973) Topological vector spaces. Notes on Mathematics and its Applications. Gordon & Breach Science Publishers, New York 22.

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Tautological Control Systems by Andrew Lewis

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