Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control
<p/> <p>This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are co...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2009/348242 |
| _version_ | 1811268394043834368 |
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| author | Huang Tingwen Li Chuandong |
| author_facet | Huang Tingwen Li Chuandong |
| author_sort | Huang Tingwen |
| collection | DOAJ |
| description | <p/> <p>This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient) small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.</p> |
| first_indexed | 2024-04-12T21:21:00Z |
| format | Article |
| id | doaj.art-056cff4b8cec41cb901121305b2416fa |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-12T21:21:00Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-056cff4b8cec41cb901121305b2416fa2022-12-22T03:16:17ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-0120091348242Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent ControlHuang TingwenLi Chuandong<p/> <p>This paper studies the exponential stability of a class of periodically time-switched nonlinear systems. Three cases of such systems which are composed, respectively, of a pair of unstable subsystems, of both stable and unstable subsystems, and of a pair of stable systems, are considered. For the first case, the proposed result shows that there exists periodically switching rule guaranteeing the exponential stability of the whole system with (sufficient) small switching period if there is a Hurwitz linear convex combination of two uncertain linear systems derived from two subsystems by certain linearization. For the second case, we present two general switching criteria by means of multiple and single Lyapunov function, respectively. We also investigate the stability issue of the third case, and the switching criteria of exponential stability are proposed. The present results for the second case are further applied to the periodically intermittent control. Several numerical examples are also given to show the effectiveness of theoretical results.</p>http://www.journalofinequalitiesandapplications.com/content/2009/348242 |
| spellingShingle | Huang Tingwen Li Chuandong Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control Journal of Inequalities and Applications |
| title | Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control |
| title_full | Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control |
| title_fullStr | Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control |
| title_full_unstemmed | Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control |
| title_short | Exponential Stability of Time-Switched Two-Subsystem Nonlinear Systems with Application to Intermittent Control |
| title_sort | exponential stability of time switched two subsystem nonlinear systems with application to intermittent control |
| url | http://www.journalofinequalitiesandapplications.com/content/2009/348242 |
| work_keys_str_mv | AT huangtingwen exponentialstabilityoftimeswitchedtwosubsystemnonlinearsystemswithapplicationtointermittentcontrol AT lichuandong exponentialstabilityoftimeswitchedtwosubsystemnonlinearsystemswithapplicationtointermittentcontrol |