On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems

In this paper, we introduce a new concept of input-to-state practical h -stability ( h -ISpS) and integral input-to-state practical h -stability ( h -iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h -ISpS and h -iISpS are given based on indefinite Lyapunov functio...

Full description

Saved in:
Bibliographic Details
Published in:Mediterranean journal of mathematics 2022-12, Vol.19 (6), Article 249
Main Authors: Damak, Hanen, Hadj Taieb, Nizar, Hammami, Mohamed Ali
Format: Article
Language:English
Subjects:
Control theory
Feedback control
Liapunov functions
Mathematics
Mathematics and Statistics
Nonlinear control
Nonlinear systems
Stability analysis
Time varying control systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83
cites cdi_FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83
container_end_page
container_issue 6
container_start_page
container_title Mediterranean journal of mathematics
container_volume 19
creator Damak, Hanen
Hadj Taieb, Nizar
Hammami, Mohamed Ali
description In this paper, we introduce a new concept of input-to-state practical h -stability ( h -ISpS) and integral input-to-state practical h -stability ( h -iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h -ISpS and h -iISpS are given based on indefinite Lyapunov functions. The practical h -stability analysis is accomplished with the help of scalar practical h -stable functions. Our main result provides conditions for h -ISpS of perturbed, cascaded and interconnected systems. Furthermore, a feedback control law is provided for a class of nonlinear control systems by which the closed-loop system is h -iISpS with respect to disturbances acting in the input. Some examples are given to illustrate the obtained results.
doi_str_mv 10.1007/s00009-022-02179-z
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2725048243</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2725048243</sourcerecordid><originalsourceid>FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83</originalsourceid><addsrcrecordid>eNp9UMFKAzEQDaJgrf6Ap4DnaDbJJrtHKWorxQqtXkM2TWrKNluT9NB-vakrenNgmGF4783jAXBd4NsCY3EXca4aYUJyF6JGhxMwKDjHqGQlO_3dGT8HFzGuMSZ1QckAPM88nPjtLqHUoXlSycDXoHRyWrXw43hpXOvSHtouwJfOt84bFeDCbQx6V2Hv_ArO9zGZTbwEZ1a10Vz9zCF4e3xYjMZoOnuajO6nSBNWJ8SrmhmLG8vsslaiIrxZVpg1Qmf3SqmyJksuONGmKqnOLjGlotLMUspMYSs6BDe97jZ0nzsTk1x3u-DzS0kEKTGrCKMZRXqUDl2MwVi5DW6THcsCy2Nmss9M5q_yOzN5yCTak2IG-5UJf9L_sL4AgRhukg</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2725048243</pqid></control><display><type>article</type><title>On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems</title><source>Springer Link</source><creator>Damak, Hanen ; Hadj Taieb, Nizar ; Hammami, Mohamed Ali</creator><creatorcontrib>Damak, Hanen ; Hadj Taieb, Nizar ; Hammami, Mohamed Ali</creatorcontrib><description>In this paper, we introduce a new concept of input-to-state practical h -stability ( h -ISpS) and integral input-to-state practical h -stability ( h -iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h -ISpS and h -iISpS are given based on indefinite Lyapunov functions. The practical h -stability analysis is accomplished with the help of scalar practical h -stable functions. Our main result provides conditions for h -ISpS of perturbed, cascaded and interconnected systems. Furthermore, a feedback control law is provided for a class of nonlinear control systems by which the closed-loop system is h -iISpS with respect to disturbances acting in the input. Some examples are given to illustrate the obtained results.</description><identifier>ISSN: 1660-5446</identifier><identifier>EISSN: 1660-5454</identifier><identifier>DOI: 10.1007/s00009-022-02179-z</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Control theory ; Feedback control ; Liapunov functions ; Mathematics ; Mathematics and Statistics ; Nonlinear control ; Nonlinear systems ; Stability analysis ; Time varying control systems</subject><ispartof>Mediterranean journal of mathematics, 2022-12, Vol.19 (6), Article 249</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83</citedby><cites>FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83</cites><orcidid>0000-0002-9347-4525</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>315,786,790,27957,27958</link.rule.ids></links><search><creatorcontrib>Damak, Hanen</creatorcontrib><creatorcontrib>Hadj Taieb, Nizar</creatorcontrib><creatorcontrib>Hammami, Mohamed Ali</creatorcontrib><title>On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems</title><title>Mediterranean journal of mathematics</title><addtitle>Mediterr. J. Math</addtitle><description>In this paper, we introduce a new concept of input-to-state practical h -stability ( h -ISpS) and integral input-to-state practical h -stability ( h -iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h -ISpS and h -iISpS are given based on indefinite Lyapunov functions. The practical h -stability analysis is accomplished with the help of scalar practical h -stable functions. Our main result provides conditions for h -ISpS of perturbed, cascaded and interconnected systems. Furthermore, a feedback control law is provided for a class of nonlinear control systems by which the closed-loop system is h -iISpS with respect to disturbances acting in the input. Some examples are given to illustrate the obtained results.</description><subject>Control theory</subject><subject>Feedback control</subject><subject>Liapunov functions</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear control</subject><subject>Nonlinear systems</subject><subject>Stability analysis</subject><subject>Time varying control systems</subject><issn>1660-5446</issn><issn>1660-5454</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9UMFKAzEQDaJgrf6Ap4DnaDbJJrtHKWorxQqtXkM2TWrKNluT9NB-vakrenNgmGF4783jAXBd4NsCY3EXca4aYUJyF6JGhxMwKDjHqGQlO_3dGT8HFzGuMSZ1QckAPM88nPjtLqHUoXlSycDXoHRyWrXw43hpXOvSHtouwJfOt84bFeDCbQx6V2Hv_ArO9zGZTbwEZ1a10Vz9zCF4e3xYjMZoOnuajO6nSBNWJ8SrmhmLG8vsslaiIrxZVpg1Qmf3SqmyJksuONGmKqnOLjGlotLMUspMYSs6BDe97jZ0nzsTk1x3u-DzS0kEKTGrCKMZRXqUDl2MwVi5DW6THcsCy2Nmss9M5q_yOzN5yCTak2IG-5UJf9L_sL4AgRhukg</recordid><startdate>20221201</startdate><enddate>20221201</enddate><creator>Damak, Hanen</creator><creator>Hadj Taieb, Nizar</creator><creator>Hammami, Mohamed Ali</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-9347-4525</orcidid></search><sort><creationdate>20221201</creationdate><title>On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems</title><author>Damak, Hanen ; Hadj Taieb, Nizar ; Hammami, Mohamed Ali</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Control theory</topic><topic>Feedback control</topic><topic>Liapunov functions</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear control</topic><topic>Nonlinear systems</topic><topic>Stability analysis</topic><topic>Time varying control systems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Damak, Hanen</creatorcontrib><creatorcontrib>Hadj Taieb, Nizar</creatorcontrib><creatorcontrib>Hammami, Mohamed Ali</creatorcontrib><collection>CrossRef</collection><jtitle>Mediterranean journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Damak, Hanen</au><au>Hadj Taieb, Nizar</au><au>Hammami, Mohamed Ali</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems</atitle><jtitle>Mediterranean journal of mathematics</jtitle><stitle>Mediterr. J. Math</stitle><date>2022-12-01</date><risdate>2022</risdate><volume>19</volume><issue>6</issue><artnum>249</artnum><issn>1660-5446</issn><eissn>1660-5454</eissn><abstract>In this paper, we introduce a new concept of input-to-state practical h -stability ( h -ISpS) and integral input-to-state practical h -stability ( h -iISpS) for nonlinear time-varying systems. Necessary and sufficient conditions for h -ISpS and h -iISpS are given based on indefinite Lyapunov functions. The practical h -stability analysis is accomplished with the help of scalar practical h -stable functions. Our main result provides conditions for h -ISpS of perturbed, cascaded and interconnected systems. Furthermore, a feedback control law is provided for a class of nonlinear control systems by which the closed-loop system is h -iISpS with respect to disturbances acting in the input. Some examples are given to illustrate the obtained results.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00009-022-02179-z</doi><orcidid>https://orcid.org/0000-0002-9347-4525</orcidid></addata></record>
fulltext fulltext
identifier ISSN: 1660-5446
ispartof Mediterranean journal of mathematics, 2022-12, Vol.19 (6), Article 249
issn 1660-5446
1660-5454
language eng
recordid cdi_proquest_journals_2725048243
source Springer Link
subjects Control theory
Feedback control
Liapunov functions
Mathematics
Mathematics and Statistics
Nonlinear control
Nonlinear systems
Stability analysis
Time varying control systems
title On Input-to-State Practical h-Stability for Nonlinear Time-Varying Systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-09-23T01%3A25%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Input-to-State%20Practical%20h-Stability%20for%20Nonlinear%20Time-Varying%20Systems&rft.jtitle=Mediterranean%20journal%20of%20mathematics&rft.au=Damak,%20Hanen&rft.date=2022-12-01&rft.volume=19&rft.issue=6&rft.artnum=249&rft.issn=1660-5446&rft.eissn=1660-5454&rft_id=info:doi/10.1007/s00009-022-02179-z&rft_dat=%3Cproquest_cross%3E2725048243%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c249t-6894ef0bf4fd9a7826bd804b7c022aaa592d6762ce853c91303378c4f334e1f83%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2725048243&rft_id=info:pmid/&rfr_iscdi=true