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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| Vydáno v: | Automatica (Oxford) Ročník 50; číslo 7; s. 1757 - 1779 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Kidlington
Elsevier Ltd
01.07.2014
Elsevier |
| Témata: | |
| ISSN: | 0005-1098, 1873-2836 |
| On-line přístup: | Získat plný text |
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| Abstract | 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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| AbstractList | 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. |
| Author | Tucsnak, Marius Weiss, George |
| Author_xml | – sequence: 1 givenname: Marius surname: Tucsnak fullname: Tucsnak, Marius email: Marius.Tucsnak@univ-lorraine.fr organization: Université de Lorraine, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506; CNRS, Institut Elie Cartan de Lorraine, UMR 7502, Vandoeuvre-lès-Nancy, F-54506; INRIA, Villers-lès-Nancy, F-54600, France – sequence: 2 givenname: George surname: Weiss fullname: Weiss, George email: gweiss@eng.tau.ac.il organization: School of Electrical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Well-posed systems—The LTI case and beyond |
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