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Author: Ulrich Krause
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110365693
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences. "The author has greatly expanded the field of positive systems in surprising ways." - Prof. Dr. David G. Luenberger, Stanford University(USA)
Author: Ulrich Krause
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110365693
Category : Mathematics
Languages : en
Pages : 366
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Book Description
This book provides a systematic, rigorous and self-contained treatment of positive dynamical systems. A dynamical system is positive when all relevant variables of a system are nonnegative in a natural way. This is in biology, demography or economics, where the levels of populations or prices of goods are positive. The principle also finds application in electrical engineering, physics and computer sciences. "The author has greatly expanded the field of positive systems in surprising ways." - Prof. Dr. David G. Luenberger, Stanford University(USA)
Author: Franco Blanchini
Publisher:
ISBN: 9781680830705
Category : Computers
Languages : en
Pages : 190
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Book Description
Positive systems are an important class of systems that frequently arise in application areas, such as in the chemical process industry, electronic circuit design, communication networks, and biology. The study of the stability of such systems differs from standard systems in that the analysis focuses only on the trajectories generated under positivity constraints. Switched positive systems also arise in a variety of applications. Examples can be found in TCP congestion control, in processes described by non-homogeneous Markov chains, in image processing, in biochemical networks, and so on. In comparison to general switched systems, that have received a lot of attention in the past years, the theory for positive switched systems is still in its infancy. Switched Positive Linear Systems studies the stability, performance evaluation, stabilization via switching control, and optimal control of (continuous-time and linear) positive switched systems. It provides a review of the results that have already been established in the literature. Other results, especially those related to norm computation and optimization, are new and are presented integrated with previous ones. Switched Positive Linear Systems provides a comprehensive and timely introduction to the study of such systems. Readers who are new to the topic will find everything required to understand such systems in a concise and accessible form.
Author: Tadeusz Kaczorek
Publisher: Springer Science & Business Media
ISBN: 9781852335083
Category : Computers
Languages : en
Pages : 450
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Book Description
This text is devoted to the positive multivariable 1D and 2D linear, time-invariant, finite-dimensional system. The book is based on the author's lectures for Ph.D. students, delivered at Warsaw University of Technology in the academic year 1999/2000. The book consists of two parts; the first part is devoted to the 1D positive linear systems and the second to the 2D positive linear systems described by the Rosser model and the Fornasini-Marchesini models. Definitions, basic properties and theorems concerning positive matrices and graphs are presented; the externally and internally positive linear continuous-time and discrete-time linear systems are considered; and the reachability, controlability and observability of positive linear systems are discussed. The realisation problem for positive 1D and 2D systems is also considered, and the 2D models of externally and internally positive and their properties and controllability and minimum energy control of positive 2D systems are investigated.
Author: James Lam
Publisher: Springer
ISBN: 3030043274
Category : Technology & Engineering
Languages : en
Pages : 331
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Book Description
This book presents high-quality original contributions on positive systems, including those with positivity in compartmental switched systems, Markovian jump systems, Boolean networks, interval observer design, fault detection, and delay systems. It comprises a selection of the best papers from POSTA 2018, the 6th International Conference on Positive Systems, which was held in Hangzhou, China, in August 2018. The POSTA conference series represents a targeted response to the growing need for research that reports on and critically discusses a wide range of topics concerning the theory and applications of positive systems. The book offers valuable insights for researchers in applied mathematics, control theory and their applications.
Author: Wassim M. Haddad
Publisher: Princeton University Press
ISBN: 0691190143
Category : Mathematics
Languages : en
Pages : 744
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Book Description
A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.
Author: King-Yeung Lam
Publisher: Springer Nature
ISBN: 3031204220
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This book introduces some basic mathematical tools in reaction-diffusion models, with applications to spatial ecology and evolutionary biology. It is divided into four parts. The first part is an introduction to the maximum principle, the theory of principal eigenvalues for elliptic and periodic-parabolic equations and systems, and the theory of principal Floquet bundles. The second part concerns the applications in spatial ecology. We discuss the dynamics of a single species and two competing species, as well as some recent progress on N competing species in bounded domains. Some related results on stream populations and phytoplankton populations are also included. We also discuss the spreading properties of a single species in an unbounded spatial domain, as modeled by the Fisher-KPP equation. The third part concerns the applications in evolutionary biology. We describe the basic notions of adaptive dynamics, such as evolutionarily stable strategies and evolutionary branching points, in the context of a competition model of stream populations. We also discuss a class of selection-mutation models describing a population structured along a continuous phenotypical trait. The fourth part consists of several appendices, which present a self-contained treatment of some basic abstract theories in functional analysis and dynamical systems. Topics include the Krein-Rutman theorem for linear and nonlinear operators, as well as some elements of monotone dynamical systems and abstract competition systems. Most of the book is self-contained and it is aimed at graduate students and researchers who are interested in the theory and applications of reaction-diffusion equations.
Author: Wassim M. Haddad
Publisher: Princeton University Press
ISBN: 1400832241
Category : Mathematics
Languages : en
Pages : 624
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Book Description
This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systems presents the most complete treatment available of system solution properties, Lyapunov stability analysis, dissipativity theory, and optimal and adaptive control for these systems, addressing continuous-time, discrete-time, and hybrid nonnegative system theory. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers, as well as for researchers and graduate students who want to understand the behavior of nonnegative and compartmental dynamical systems that arise in areas such as biomedicine, demographics, epidemiology, pharmacology, telecommunications, transportation, thermodynamics, networks, heat transfer, and power systems.
Author: Ju H. Park
Publisher: Springer Nature
ISBN: 3030491234
Category : Technology & Engineering
Languages : en
Pages : 548
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Book Description
This edited book introduces readers to new analytical techniques and controller design schemes used to solve the emerging “hottest” problems in dynamic control systems and networks. In recent years, the study of dynamic systems and networks has faced major changes and challenges with the rapid advancement of IT technology, accompanied by the 4th Industrial Revolution. Many new factors that now have to be considered, and which haven’t been addressed from control engineering perspectives to date, are naturally emerging as the systems become more complex and networked. The general scope of this book includes the modeling of the system itself and uncertainty elements, examining stability under various criteria, and controller design techniques to achieve specific control objectives in various dynamic systems and networks. In terms of traditional stability matters, this includes the following special issues: finite-time stability and stabilization, consensus/synchronization, fault-tolerant control, event-triggered control, and sampled-data control for classical linear/nonlinear systems, interconnected systems, fractional-order systems, switched systems, neural networks, and complex networks. In terms of introducing graduate students and professional researchers studying control engineering and applied mathematics to the latest research trends in the areas mentioned above, this book offers an excellent guide.
Author: Francesco Amato
Publisher: John Wiley & Sons
ISBN: 1119140528
Category : Technology & Engineering
Languages : en
Pages : 184
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Book Description
Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H∞ control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.
Author: Sandra Pinelas
Publisher: Springer Science & Business Media
ISBN: 1461473330
Category : Mathematics
Languages : en
Pages : 639
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Book Description
The volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada – Azores, from July 4-8, 2011 in honor of Professor Ravi P. Agarwal. The objective of the gathering was to bring together researchers in the fields of differential & difference equations and to promote the exchange of ideas and research. The papers cover all areas of differential and difference equations with a special emphasis on applications.
