Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems
<p/> <p>This paper studies the problem of stabilization with optimal performance for dissipative DIHS (discrete-time impulsive hybrid systems). By using Lyapunov function method, conditions are derived under which the DIHS with zero inputs is GUAS (globally uniformly asymptotically stabl...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2010/278240 |
| _version_ | 1818934098990727168 |
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| author | Liu Bin Yan Lamei |
| author_facet | Liu Bin Yan Lamei |
| author_sort | Liu Bin |
| collection | DOAJ |
| description | <p/> <p>This paper studies the problem of stabilization with optimal performance for dissipative DIHS (discrete-time impulsive hybrid systems). By using Lyapunov function method, conditions are derived under which the DIHS with zero inputs is GUAS (globally uniformly asymptotically stable). These GUAS results are used to design feedback control law such that a dissipative DIHS is asymptotically stabilized and the value of a hybrid performance functional can be minimized. For the case of linear DIHS with a quadratic supply rate and a quadratic storage function, sufficient and necessary conditions of dissipativity are expressed in matrix inequalities. And the corresponding conditions of optimal quadratic hybrid performance are established. Finally, one example is given to illustrate the results.</p> |
| first_indexed | 2024-12-20T04:58:53Z |
| format | Article |
| id | doaj.art-2479c42d3cad4f89811335ba03340e24 |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-12-20T04:58:53Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-2479c42d3cad4f89811335ba03340e242022-12-21T19:52:36ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472010-01-0120101278240Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid SystemsLiu BinYan Lamei<p/> <p>This paper studies the problem of stabilization with optimal performance for dissipative DIHS (discrete-time impulsive hybrid systems). By using Lyapunov function method, conditions are derived under which the DIHS with zero inputs is GUAS (globally uniformly asymptotically stable). These GUAS results are used to design feedback control law such that a dissipative DIHS is asymptotically stabilized and the value of a hybrid performance functional can be minimized. For the case of linear DIHS with a quadratic supply rate and a quadratic storage function, sufficient and necessary conditions of dissipativity are expressed in matrix inequalities. And the corresponding conditions of optimal quadratic hybrid performance are established. Finally, one example is given to illustrate the results.</p>http://www.advancesindifferenceequations.com/content/2010/278240 |
| spellingShingle | Liu Bin Yan Lamei Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems Advances in Difference Equations |
| title | Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems |
| title_full | Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems |
| title_fullStr | Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems |
| title_full_unstemmed | Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems |
| title_short | Stabilization with Optimal Performance for Dissipative Discrete-Time Impulsive Hybrid Systems |
| title_sort | stabilization with optimal performance for dissipative discrete time impulsive hybrid systems |
| url | http://www.advancesindifferenceequations.com/content/2010/278240 |
| work_keys_str_mv | AT liubin stabilizationwithoptimalperformancefordissipativediscretetimeimpulsivehybridsystems AT yanlamei stabilizationwithoptimalperformancefordissipativediscretetimeimpulsivehybridsystems |