Skip to main content Accessibility help
×
Home
Hostname: page-component-5d6d958fb5-9cwrl Total loading time: 0.312 Render date: 2022-11-27T16:41:25.080Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "displayNetworkTab": true, "displayNetworkMapGraph": false, "useSa": true } hasContentIssue true

14 - Well-Posed Input/State/Output Systems

Published online by Cambridge University Press:  05 May 2022

Damir Z. Arov
Affiliation:
South Ukrainian Pedagogical University
Olof J. Staffans
Affiliation:
Åbo Akademi University, Finland
Get access

Summary

This chapter is devoted to the study of well-posed i/s/o systems. These systems are assumed to be solvable and to satisfy a well-posedness condition that guarantees the existence of a unique future generalized trajectory for any given initial state and input function that belongs locally to L2. Although it is not obvious from the definition, every well-posed i/s/o system is internally well-posed, i.e., it has a nonempty resolvent set-and its main operator generates a C0 semigroup. Semi-bounded i/s/o systems are well-posed. The class of well-posed i/s/o systems is the largest class in this book for which can to prove connections between time and frequency domain results that are analogous to those established in Chapter 8 for the class of semi-bounded i/s/o systems. At the end of this chapter we define the notion of a scattering passive system, and show that scattering passive systems are well-posed. A scattering passive system is characterized by the fact that it is regular, and its system operator is maximally scattering dissipative. Well-posed s/s systems are discussed in Chapter 15.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×