An application of forward difference method in robust stability of discrete uncertainty system with delays
Abstract This paper deals with the problems of robust stability for a class of uncertainty parameter systems with delays. By using a new Lyapunov–Krasovskii functional, quadratic inequality, and Schur complement technique, two conditions are developed to guarantee the robust stability of a class of...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-1991-x |
| _version_ | 1819315494841221120 |
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| author | Xianghui Zhou Zizong Yan |
| author_facet | Xianghui Zhou Zizong Yan |
| author_sort | Xianghui Zhou |
| collection | DOAJ |
| description | Abstract This paper deals with the problems of robust stability for a class of uncertainty parameter systems with delays. By using a new Lyapunov–Krasovskii functional, quadratic inequality, and Schur complement technique, two conditions are developed to guarantee the robust stability of a class of discrete systems with uncertainty parameters in terms of the linear matrix inequality (LMI). By applying the forward difference method and via a quadratic cost function, the criteria of LMI are obtained by the input control u(k)=0 $u(k)=0$ and u(k)=Kx(k) $u(k)=Kx(k)$; meanwhile, the bounds of cost function are established. The feedback control gain is designed to ensure the robust stability of the closed-loop system. A numerical example and simulation figures are provided to illustrate the effectiveness and potential of the proposed techniques and results. |
| first_indexed | 2024-12-24T10:01:00Z |
| format | Article |
| id | doaj.art-e5c0c027be584a369f03c45c7e411415 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-24T10:01:00Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e5c0c027be584a369f03c45c7e4114152022-12-21T17:01:03ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019111110.1186/s13662-019-1991-xAn application of forward difference method in robust stability of discrete uncertainty system with delaysXianghui Zhou0Zizong Yan1School of Information and Mathematics, Yangtze UniversitySchool of Information and Mathematics, Yangtze UniversityAbstract This paper deals with the problems of robust stability for a class of uncertainty parameter systems with delays. By using a new Lyapunov–Krasovskii functional, quadratic inequality, and Schur complement technique, two conditions are developed to guarantee the robust stability of a class of discrete systems with uncertainty parameters in terms of the linear matrix inequality (LMI). By applying the forward difference method and via a quadratic cost function, the criteria of LMI are obtained by the input control u(k)=0 $u(k)=0$ and u(k)=Kx(k) $u(k)=Kx(k)$; meanwhile, the bounds of cost function are established. The feedback control gain is designed to ensure the robust stability of the closed-loop system. A numerical example and simulation figures are provided to illustrate the effectiveness and potential of the proposed techniques and results.http://link.springer.com/article/10.1186/s13662-019-1991-xRobust stabilityForward differenceUncertainty systemSchur complement |
| spellingShingle | Xianghui Zhou Zizong Yan An application of forward difference method in robust stability of discrete uncertainty system with delays Advances in Difference Equations Robust stability Forward difference Uncertainty system Schur complement |
| title | An application of forward difference method in robust stability of discrete uncertainty system with delays |
| title_full | An application of forward difference method in robust stability of discrete uncertainty system with delays |
| title_fullStr | An application of forward difference method in robust stability of discrete uncertainty system with delays |
| title_full_unstemmed | An application of forward difference method in robust stability of discrete uncertainty system with delays |
| title_short | An application of forward difference method in robust stability of discrete uncertainty system with delays |
| title_sort | application of forward difference method in robust stability of discrete uncertainty system with delays |
| topic | Robust stability Forward difference Uncertainty system Schur complement |
| url | http://link.springer.com/article/10.1186/s13662-019-1991-x |
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