Well-posed systems—The LTI case and beyond

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 linear systems, some of the availab...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 50; no. 7; pp. 1757 - 1779
Main Authors: Tucsnak, Marius, Weiss, George
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.07.2014
Elsevier
Subjects:
Analysis of PDEs
Analytical and numerical techniques
Applied sciences
Burgers equation
Computational methods in fluid dynamics
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Criteria
Exact sciences and technology
Feedback
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Heat equation
Heat transfer
Impedance passive system
Linear systems
Local well-posedness
Mathematical analysis
Mathematics
Navier-Stokes equations
Non-linear feedback
Nonlinearity
Operator semigroup
Optimization and Control
Physics
Recall
Regular linear system
Scattering conservative system
Scattering passive system
Wave equation
Well posed problems
Well-posed linear system
Scattering conservative system
Wave equation
Navier–Stokes equations
Well-posed linear system
Operator semigroup
Heat equation
Non-linear feedback
Scattering passive system
Local well-posedness
Impedance passive system
Burgers equation
Regular linear system
Generalized solution
Non linear control
Feedback regulation
Passive system
Modeling
Conservative system
Linear time invariant system
Feedback
Navier Stokes equation
Well posed problem
Semigroup
Non linear system
Global local method
Linear system
Non linear effect
Heat transfer
Navier-Stokes equations
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Description
Summary: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 linear systems, some of the available linear feedback theory. Motivated by physical examples, we recall the concepts of impedance passive and scattering passive systems, conservative systems and systems with a special structure that belong to these classes. We illustrate this theory by examples of systems governed by heat and wave equations. We develop local and global well-posedness results for LTI systems with nonlinear (in particular, bilinear) feedback, by extracting the abstract idea behind various proofs in the literature. We apply these abstract results to derive well-posedness results for the Burgers and Navier–Stokes equations.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2014.04.016