5 edition of **Stability of finite and infinite dimensional systems** found in the catalog.

- 339 Want to read
- 39 Currently reading

Published
**1998** by Kluwer Academic Publishers in Boston .

Written in English

- Automatic control,
- Control theory,
- Differential equations, Partial,
- Stability

**Edition Notes**

Includes bibliographical references and index.

Statement | by Michael I. Gilʼ. |

Series | The Kluwer international series in engineering and computer science ;, SECS 455 |

Classifications | |
---|---|

LC Classifications | TJ213 .G496 1998 |

The Physical Object | |

Pagination | xviii, 354 p. ; |

Number of Pages | 354 |

ID Numbers | |

Open Library | OL367009M |

ISBN 10 | 0792382218 |

LC Control Number | 98027508 |

It deals with both finite- and infinite-dimensional nonconservative systems and covers the fundamentals of the theory, including such topics as Lyapunov stability and linear stability analysis, Hamiltonian and gyroscopic systems, reversible and circulatory systems, influence of structure of forces. For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral input-to-state stability. We provide two proofs of this fact. One applies to general systems over Banach spaces. The other is restricted to Hilbert spaces, but is more constructive and results in an explicit form of iISS Lyapunov by: The first attempt at infinite-dimensional feedback design in the field of control systems, the Smith predictor, has remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or. Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integrated fashion. The authors' primary aim is to write an introductory textbook 5/5(2).

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The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations.

Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on. Stability of Finite and Infinite Dimensional Systems (The Springer International Series in Engineering and Computer Science) [Michael I.

Gil'] on *FREE* shipping on qualifying offers. The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theoryCited by: The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and differential-delay equations.

Stability of Finite and Infinite Dimensional Systems is the. Get this from a library. Stability of finite and infinite dimensional systems. [M Stability of finite and infinite dimensional systems book Gilʹ] -- The aim of Stability of Finite and Infinite Dimensional Systems is to provide new tools for specialists in control system theory, stability theory of ordinary and partial differential equations, and.

Stability of Finite and Infinite Dimensional Systems is the first book that gives a systematic exposition of the approach to stability analysis which is based on estimates for matrix-valued and operator-valued functions, allowing us to investigate various classes of finite and infinite dimensional systems from the unified viewpoint.

Stability Stability of finite and infinite dimensional systems book Finite and Infinite Dimensional Systems is intended not only for specialists in stability theory, but for anyone interested in various applications who has had at least a first year Author: Michael Gil. The model consists of the power preserving interconnection between two infinite dimensional systems describing the beam's motion and deformation with.

In this paper we are concerned with stability problems for infinite dimensional systems. First we review the theory for linear systems where the dynamics are governed by strongly continuous semigroups and then use these results to obtain globial existence and stability results for nonlinear by: The book covers the Stability of finite and infinite dimensional systems book four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems defined on general metric spaces * Stability of finite and infinite dimensional systems book of this stability theory to finite-dimensional dynamical systems.

- Specialization of this stability theory to finite-dimensional dynamical systems - Specialization of this stability theory to infinite-dimensional dynamical systems.

Replete with examples and requiring only a basic knowledge of linear algebra, analysis, and differential equations, this book can be used as a textbook for graduate courses in. In this paper we are concerned with stability problems for infinite dimensional systems.

First we review the theory for linear systems where the dynamics are governed by strongly continuous semigroups and then use these results to obtain globial existence Stability of finite and infinite dimensional systems book stability results for nonlinear systems.

We also consider the problem of designing feedback controls to enhance Cited by: Originally published inFinite Dimensional Linear Systems is a classic textbook that provides a solid foundation for learning about dynamical systems and encourages students to develop a reliable intuition for problem solving.

The theory of linear systems has been the bedrock of control theory for 50 years and has served as the springboard for many significant developments, all Price Range: $ - $ The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability and stability.

This theory is far more difficult for infinite-dimensional systems such as systems with time delay and distributed parameter by: Purchase Infinite Dimensional Linear Control Systems, Volume - 1st Edition.

Print Book & E-Book. ISBNStability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schrödinger equations with boundary control and observation.

The analysis is based on the frequency domain method which gives new results for second order port Cited by: The Nehari extension problem for State linear Systems Exercises Notes and references 9 Robust Finite-Dimensional Controller Synthesis Closed-loop stability and coprime factorizations Robust stabilization of uncertain Systems Robust stabilization under additive uncertainty Finite Dimensional Linear Systems by Roger W.

Brockett,available at Book Depository with free delivery worldwide. Infinite Dimensional Linear Systems Theory. R.F. Curtain, A.J. Pritchard.

Springer Berlin Heidelberg, Aug 1, - Computers - pages. 0 Reviews. From inside the book. What people are saying - Write a review. We haven't found any reviews in the usual places. Contents. INTRODUCTION. 1: Examples of infinite dimensional systems.

STABILITY THEORY FOR COUNTABLY INFINITE SYSTEMS R. Miller 1 ' 2 Mathematics Department Iowa State University Ames, Iowa A. Michel 3 ' 4 Electrical Engineering Department and Engineering Research Ames, Iowa Institute Iowa State University INTRODUCTION In the present paper we establish new stability results for a class of Author: R.K.

Miller, A.N. Michel. (Please note: book is copyrighted by Springer-Verlag. Springer has kindly allowed me to place a copy on the web, as a reference and for ease of web searches. Please consider buying your own hardcopy.) Precise reference: Eduardo D.

Sontag, Mathematical Control Theory: Deterministic Finite Dimensional Systems. Therefore, there is a need for a reference book which presents these restllts in an integrated fashion. Complementing the existing books, e.

[1]. [41]. and []. this book reports some recent achievements in stability and feedback stabilization of infinite dimensional systems. Arada, Nadir and Raymond, Jean-Pierre Minimax Control of Parabolic Systems with State Constraints. SIAM Journal on Control and Optimization, Vol.

38, Issue. 1, p. Cited by: In this note, we generalize the results from Narendra and Balakrishnan (IEEE Trans. Automatic Control 39 () ) to the infinite-dimensional system theoretic setting.

The paper gives results on the stability of a switching system of the form x ˙ (t) = A i x (t), i ∈ {1, 2}, when the infinitesimal generators A 1 and A 2 commute. In Cited by: Part III covers design and applications book will benefit the academic research and graduate student interested in the mathematics of Lyapunov equations and variable-structure control, stability analysis and robust feedback design for discontinuous systems.

It will also serve the practitioner working with applications of such systems. The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view.

The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability. As a natural consequence of these observations, a new direction of research has arisen: detection and analysis of finite dimensional dynamical characteristics of infinite-dimensional systems.

This book represents the proceedings of an AMS-IMS-SIAM Summer Research Conference, held in July, at the University of Colorado at Boulder. The second edition of this textbook provides a single source for the analysis of system models represented by continuous-time and discrete-time, finite-dimensional and infinite-dimensional, and continuous and discontinuous dynamical systems.

As in the finite-dimensional case the transfer function is defined through the Laplace transform (continuous-time) or Z-transform (discrete-time). Whereas in the finite-dimensional case the transfer function is a proper rational function, the infinite-dimensionality of the state space leads to irrational functions (which are however still.

Representation and Control of Infinite Dimensional Systems. Book Title:Representation and Control of Infinite Dimensional Systems. The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from the theoretical and design points of view.

ov Dissipative Systems Infinite-Dimensional Introduction Theory I. Chueshov Introduction to the Theory of InfiniteDimensional Dissipative Systems ––64–5 ORDERFile Size: 2MB.

The paper is devoted to full stability of optimal solutions in general settings of finite-dimensional optimization with applications to particular models of constrained optimization problems, including those of conic and specifically semidefinite by: Theories of the infinite dimensional dynamical systems have also found more and more important applications in physical, chemical, and life sciences.

This book collects 19 papers from 48 invited lecturers to the International Conference on Infinite Dimensional Dynamical Systems held at York University, Toronto, in September of Author: John Mallet-Paret.

Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and : Mark J.

Balas, Susan A. Frost. The root locus is an important tool for analysing the stability and time constants of linear finite-dimensional systems as a parameter, often the gain, is varied.

However, many systems are modelled by partial differential equations or delay equations. These systems evolve on an infinite-dimensional space and their transfer functions are not rational. We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives.

Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class. Infinite dimensional systems can be used to describe many phenomena in the real world.

As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state.

We are. Infinite-Dimensional Dynamical Systems by James C. Robinson,available at Book Depository with free delivery worldwide.4/5(4). One of the necessary conditions is a constraint on the non-minimum phase zeros of a plant and the other is a constraint on the unstable poles of the plant.

The necessary condition is automatically satisfied by every finite dimensional plant, so our result is only interesting for infinite dimensional plants.

Input-to-state stability (ISS) is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymptotically stable in the absence of external inputs and if its trajectories are bounded by a function of the size of the input for all sufficiently large times.

Global attractors of infinite-dimensional dynamical systems and their stability under multi-valued perturbations: - Lunch; - Yuan Wang: On notions of input-to-output stability for systems with time-delays: - Sergey Dashkovskiy: Stability of systems with dynamics depending on the maximum of solution over a.

An introduction to infinite-dimensional linear systems theory An introduction to pdf linear systems theory Banks, S.P. It is often said that the study of infinite-dimensional systems associated with partial differential equations or delay differential equations is unnecessary since one can always discretize and use finite .Book Description.

Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, differential equations, optimization, and approximation.A robust control scheme for tracking of periodic signals, ebook of ebook finite number of sinusoids, by uncertain exponentially stable infinite dimensional linear systems is presented.

The scheme consists in constructing a cascade interconnection of the stable linear system and a partitioning filter and augmenting this cascade system with a Cited by: 3.