Invariance and System Theory PDF Download

Author: Allen Tannenbaum
Publisher: Springer
ISBN: 3540385363
Category : Science
Languages : en
Pages : 171

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Author: Giuseppe Basile
Publisher:
ISBN:
Category : Linear systems
Languages : en
Pages : 632

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Book Description
Using a geometric approach to system theory, this work discusses controlled and conditioned invariance to geometrical analysis and design of multivariable control systems, presenting new mathematical theories, new approaches to standard problems and applied mathematics topics.

Author: Allen Tannenbaum
Publisher:
ISBN: 9783662201275
Category :
Languages : en
Pages : 176

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Book Description

Author: Christoph Kawan
Publisher: Springer
ISBN: 3319012886
Category : Mathematics
Languages : en
Pages : 290

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Book Description
This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.

Author: H.E.A. Eddy Campbell
Publisher: Springer Science & Business Media
ISBN: 3642174043
Category : Mathematics
Languages : en
Pages : 233

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Book Description
This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.

Author: Oliver Edmunds Glenn
Publisher:
ISBN:
Category : Invariants
Languages : en
Pages : 268

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Author: Malte Henkel
Publisher: Springer Science & Business Media
ISBN: 3662039370
Category : Science
Languages : en
Pages : 433

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Book Description
Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur bulence and may even extend to the quark-gluon plasma and the early uni verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal ing, provided only that angles remain unchanged.

Author: Isukapalli Gopala Sarma
Publisher:
ISBN:
Category : Automatic control
Languages : en
Pages : 428

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Author: Fritz Colonius
Publisher: Springer Science & Business Media
ISBN: 1461201799
Category : Technology & Engineering
Languages : en
Pages : 320

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Book Description
This new edited book focuses on the contemporary developments and results in mathematical systems theory and control. It is a book in honor of Diederich Hinrichsen, for his fundamental contributions and achievements in the fields of linear systems theory and control theory and for his long term achievements in establishing mathematical systems theory in Germany. The book includes invited, peer-reviewed, authoritative expositions and surveys of these fields, presented by leading international researchers. A key theme of the book is the stability and robustness of linear and nonlinear systems using the concepts of stability radii and spectral value sets. Chapters survey recent advances in linear and nonlinear systems theory, including parameterization problems and behaviors of linear systems, convolutional codes, and complementary systems and hybrid systems. In addition, the volume examines controllability and stabilization of infinite dimensional systems (allowing for hysteresis nonlinearities) with functional analytic and algebraic approaches. Features and topics include: * linear and nonlinear systems theory * control theory and applications * robust stability of multivariate polynomials * stability radii of slowly time-varying systems * invariance radius for nonlinear systems * parametrization of conditioned invariant subspaces The book is an essential resource for all researchers and professionals in applied mathematics and control engineering who are.

Author: Agostino Martinelli
Publisher: SIAM
ISBN: 1611976251
Category : Mathematics
Languages : en
Pages : 277

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Book Description
This book is about nonlinear observability. It provides a modern theory of observability based on a new paradigm borrowed from theoretical physics and the mathematical foundation of that paradigm. In the case of observability, this framework takes into account the group of invariance that is inherent to the concept of observability, allowing the reader to reach an intuitive derivation of significant results in the literature of control theory. The book provides a complete theory of observability and, consequently, the analytical solution of some open problems in control theory. Notably, it presents the first general analytic solution of the nonlinear unknown input observability (nonlinear UIO), a very complex open problem studied in the 1960s. Based on this solution, the book provides examples with important applications for neuroscience, including a deep study of the integration of multiple sensory cues from the visual and vestibular systems for self-motion perception. Observability: A New Theory Based on the Group of Invariance is the only book focused solely on observability. It provides readers with many applications, mostly in robotics and autonomous navigation, as well as complex examples in the framework of vision-aided inertial navigation for aerial vehicles. For these applications, it also includes all the derivations needed to separate the observable part of the system from the unobservable, an analysis with practical importance for obtaining the basic equations for implementing any estimation scheme or for achieving a closed-form solution to the problem. This book is intended for researchers in robotics and automation, both in academia and in industry. Researchers in other engineering disciplines, such as information theory and mechanics, will also find the book useful.