Well-Posed Linear Systems

Cover of: Well-Posed Linear Systems | Olof Staffans

Published by Cambridge University Press .

Written in English

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Subjects:

  • Cybernetics & systems theory,
  • Differential Equations,
  • Mathematics,
  • Science/Mathematics,
  • Algebra - Linear,
  • Mathematics / General,
  • Linear systems,
  • Lineaire systemen.,
  • System theory,
  • gtt

Edition Notes

Encyclopedia of Mathematics and its Applications

Book details

The Physical Object
FormatHardcover
Number of Pages794
ID Numbers
Open LibraryOL7765267M
ISBN 100521825849
ISBN 109780521825849

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This is the first Well-Posed Linear Systems book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting.

It is also the first to describe the class of non-well-posed systems induced by system by: The realization (34) can be given a meaning using the theory of well-posed linear systems [66, 62, 42,64].

However, in order to prove asymptotic stability, we need a framework to give a meaning to. Well-posed linear systems. [Olof J Staffans] -- "This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting.

It is also the first to describe the. Get this from a library. Well-posed linear systems. [Olof J Staffans] -- Much of the material that the author presents is original and many results have never appeared in book form before.

A comprehensive bibliography completes this work which will be indispensable to all. The concept of well-posed system Informally speaking, a system is well-posed if on any time interval [˝;t], for any initial state x0 in the state space and anyinput function u in a specified space of functions, it has a unique state trajectory x and a unique output function y, both defined on [˝;t].Moreover, y must belong to a specified space of functions, and both x(t) and y must depend.

2 Basic properties of well-posed linear systems Motivation Definitions and basic properties Basic examples of well-posed linear systems Time discretization The growth bound Shift realizations The Lax–Phillips scattering model The Weiss notation Comments 3 Strongly.

Well-posed linear systems | Staffans O. | download | B–OK. Download books for free. Find books. For any Ï„ ≥ 0 and any Z, Hilbert space, we deï¬ ne for all u, v in L2([0,∞), Z) the following binary operator Proceedings of the 20th IFAC World Congress Toulouse, France, JulyGhislain Haine et al.

/ IFAC PapersOnLine () – Closed-loop perturbations of well-posed linear systems Author: Ghislain Haine. The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g. the work of Weiss and the book of Staffans.

This survey is an introduction to well-posed linear time-invariant (LTI) systems for non-specialists. We recall the more general concept of a system node, classical and generalized solutions of system equations, criteria for well-posedness, the subclass of regular Well-Posed Linear Systems book systems, some of the available linear feedback by: We discuss the connection between Lax—Phillips scattering theory and the theory of well-posed linear systems, and show that the latter theory is a natural extension of the former.

As a consequence of this, there is a close connection between the Lax—Phillips generator and the generators of the corresponding well-posed linear by: 3.

timization to infinite-dimensional well-posed linear systems, thus completing the work of George Weiss, Olof Staffans and others. We show that the optimal control is given by the stabilizing solution of an integral Riccati equation.

If the input operator is not maximally unbounded, then this integral Riccati equation is equivalent to the. Well Posed Initial-Value Problem. For a proper authoritative definition of ``well posed'' in the field of finite-difference schemes, see, e.g., [].The definition we will use here is less general in that it excludes amplitude growth from initial conditions which is faster than polynomial in time.

We will say that an initial-value problem is well posed if the linear system defined by the PDE. In particular, we introduce two important classes of well-posed linear systems which are central in this book and list some of their properties, which will be used in the sequel. Figure shows the hierarchy of the various classes of systems that we will encounter in this chapter.

Well Posed Initial-Value Problem. For a proper authoritative definition of ``well posed'' in the field of finite-difference schemes, see, e.g., [].The definition we will use here is less general in that it excludes amplitude growth from initial conditions which is faster than polynomial in time.

We will say that an initial-value problem is well posed if the linear system defined by the PDE. spaces. This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting.

It is also the first to describe the class of non-well-posed systems induced by system nodes. The author shows how standard finite-dimensional results from systems theory can be. The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g.

the work of Weiss and the book of Staffans. Many partial partial differential equations with boundary control and point observation can be formulated as a well-posed linear by: 1.

A distributed parameter system (as opposed to a lumped parameter system) is a system whose state space is infinite- dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are systems described by partial differential equations or by delay differential equations.

1 Linear time-invariant distributed. dimensional linear systems, the above citations from [2] are still valid. For this reason, instead of writing a long and confusing introductory section to [6] or resorting to an end-less jungle of references to various works with incompatible notations, we have decided to write this companion paper.

REGULARIZATION AND FREQUENCY{DOMAIN STABILITY OF WELL{POSED SYSTEMS YURI LATUSHKIN, TIMOTHY RANDOLPH, AND ROLAND SCHNAUBELT Abstract. We study linear control systems with unbounded control and observation operators using certain regularization techniques. This allows us to introduce a modi. Problems in nonlinear complex systems (so called chaotic systems) provide well-known examples of instability.

An ill-conditioned problem is indicated by a large condition number. If the problem is well-posed, then it stands a good chance of solution on a computer using a stable algorithm. If it is not well-posed, it needs to be re-formulated. The dynamical systems method (DSM) is a powerful computational method for solving operator equations.

With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. Staffans O.J. (): Well-Posed Linear Systems. - Book in preparation. Staffans O.J. and Weiss G.

(a): Transfer functions of regular linear systems. Part II: The system operator and the Lax-Phillips semigroup. - London: preprint.

Staffans O.J. and Weiss G. (b): Transfer functions of regular linear systems. Part III: Inversions and duality. We will say that an initial-value problem is well posed if the linear system defined by the PDE, together with any bounded initial conditions is marginally stable.

As discussed in [ ], a system is defined to be stable when its response to bounded initial conditions approaches zero as. We give a very general theorem about the equivalence of input-output stability and exponential stability of well-posed linear systems: the two are equivalent if the system is optimizable and estimatable.

We conclude that a well-posed system is exponentially stable if and only if it is dynamically stabilizable and input-output by: This is the first book dealing with well-posed infinite-dimensional linear systems with an input, a state, and an output in a Hilbert or Banach space setting.

It is also the first to describe the class of non-well-posed systems induced by system nodes. This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients.

Mainly two questions are discussed:(A) Under which conditions on lower order terms is the Cauchy problem well posed?(B) When is the Cauchy problem well posed for any lowerBrand: Springer International Publishing.

This class of systems is studied in the book (CZ95). However, it is not really \good enough" to study boundary control Finland Frequency Domain Well-Posed Linear Systems. Frame 11 of 45 Graph form of i/s/o system If S is a relation, then S maps every pair [x u] into an a ne subspace (which may be empty for some [x u]), and the equation x_(t).

Well-Posed Linear Systems (Encyclopedia of Math Staffans- Artificial Neural Networks: $ Artificial Neural Networks for Modelling and Control of Non-Linear Systems by. In particular, we show that an equivalent condition for the existence of a strong coprime factorization is that both the control and the filter algebraic Riccati equation (of an arbitrary well-posed realization) have a solution (in general unbounded and not even densely defined) and that a coupling condition involving these two solutions is Author: Mark R.

Opmeer, Olof J. Staffans. Controllability and observability of a well-posed system coupled with a finite-dimensional system coupled systems are well-posed and actually regular (this is easy). Then we address the question of exact (or approximate) The well-posed linear system d, with input function u, input space Cm.

Sinceshe has been with the University of Wuppertal, Germany, where she is a full professor in analysis. Her current research interests include the area of infinite-dimensional systems and operator theory, particularly well-posed linear systems and port-Hamiltonian systems.

The book includes a discussion of numerous topics, including: * hypertopologies, ie, topologies on the closed subsets of a metric space; * duality in linear programming problems, via cooperative game theory; * the Hahn-Banach theorem, which is a fundamental tool for the study of convex functions; * questions related to convergence of sets of nets;Format: Hardcover.

ticated and computationally intensive solutions of the resulting algebraic systems of difference equations at each time step. The present stabilized explicit scheme requires no Courant restriction on Δt, and hence would be of great value in computing mul­ tidimensional, well-posed, nonlinear parabolic equations on fine meshes, by simply.

American Mathematical Society Charles Street Providence, Rhode Island or AMS, American Mathematical Society, the tri-colored AMS logo, and Advancing research, Creating connections, are trademarks and services marks of the American Mathematical Society and registered in the U.S.

Patent and Trademark. Reciprocals of well-posed linear systems During the past decade great progress has been made in studying the class of well-posed lin-ear systems. Roughly speaking, these are generalizations of the nite-dimensional systems back to Livsic in his book [3], and indeed, although the treatment of systems there is rather di erent, the reciprocal.

Linear And Digital Systems Ps-2 8 Outlet Power Conditioner Linear And. Digital Systems Ps-2 Outlet Linear Conditioner And Power 8 Linear Systems Outlet Conditioner Digital Power And 8 Ps-2.

The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g. the work of Weiss and the book of Staffans. Many partial partial differential equations with boundary control and point observation can be formulated as a well-posed linear : Denis Matignon and Hans Zwart.

Encyclopedia of Mathematics and Its Applications Founding Editor G. Rota - Well-Posed Linear Systems Olof Staffans Frontmatter More information. Well-PosedLinearSystems OLOFSTAFFANS A catalog record for this book is available from the British LibraryCited by: Characterization of well-posedness of piecewise linear systems.

/ Imura, J.I.; van der Schaft, Arjan. Enschede: University of Twente, Department of Applied Mathematics, (Memorandum / Department of Mathematics; No. Research output: Book/Report › Report › Other research outputCited by:.

The remaining three chapters of the first half of the book focus o n linear sys-tems, beginning with a description of input/output behavior in Chapter 5.

In Chap-ter 6, we formally introduce feedback systems by demonstrating how state space control laws can be designed. This is followed in Chapter 7 by material on output feedback and estimators.A semigroup approach for the well-posedness of perturbed nonhomogeneous abstract boundary value problems is developed in this paper.

This allows us to introduce a useful variation of constant formula for the solutions. Drawing from this formula, necessary and sufficient conditions for the approximate controllability of such systems are obtained, using the feedback theory of well-posed and.Well-Posed Problems 1.

The problems discussed so far follow a pattern: Elliptic PDEs are coupled with bound-ary conditions, while hyperbolic and parabolic equations get initial-boundary and pure initial conditions. This is part of a more general pattern.

Certain types of partial differential equations go naturally with certain side conditions. Size: 52KB.

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