Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay
This paper is concerned with the delay-dependent H∞ control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/545636 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559503651897344 |
|---|---|
| author | Jinghao Li Qingling Zhang Ding Zhai Yi Zhang |
| author_facet | Jinghao Li Qingling Zhang Ding Zhai Yi Zhang |
| author_sort | Jinghao Li |
| collection | DOAJ |
| description | This paper is concerned with the delay-dependent H∞ control problem for continuous-time descriptor
Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii
functionals for different subsystems, together with delay decomposition method, a new delay-dependent
bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are
regular, impulse-free, and stochastically stable and satisfy a prescribed H∞ performance level. Since the
reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed
BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods. |
| format | Article |
| id | doaj-art-9e90c9fb27af4bd297ad99f0791549b2 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9e90c9fb27af4bd297ad99f0791549b22025-02-03T01:29:55ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/545636545636Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying DelayJinghao Li0Qingling Zhang1Ding Zhai2Yi Zhang3Institute of Systems Science, Northeastern University, Shenyang 110819, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110819, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110819, ChinaInstitute of Systems Science, Northeastern University, Shenyang 110819, ChinaThis paper is concerned with the delay-dependent H∞ control problem for continuous-time descriptor Markovian jump systems with time-varying delay. By constructing various Lyapunov-Krasovskii functionals for different subsystems, together with delay decomposition method, a new delay-dependent bounded real lemma (BRL) is derived, under which descriptor Markovian jump time-delay systems are regular, impulse-free, and stochastically stable and satisfy a prescribed H∞ performance level. Since the reciprocally convex combination approach is adopted to estimate the upper bound of the integral terms, the BRL obtained in this paper is less conservative than some existing ones. Based on the proposed BRL, a sufficient condition for the existence of state feedback controller is provided. Finally, three numerical examples are provided to demonstrate the validity of the proposed methods.http://dx.doi.org/10.1155/2013/545636 |
| spellingShingle | Jinghao Li Qingling Zhang Ding Zhai Yi Zhang Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay Journal of Applied Mathematics |
| title | Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay |
| title_full | Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay |
| title_fullStr | Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay |
| title_full_unstemmed | Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay |
| title_short | Delay-Dependent H∞ Control for Descriptor Markovian Jump Systems with Time-Varying Delay |
| title_sort | delay dependent h∞ control for descriptor markovian jump systems with time varying delay |
| url | http://dx.doi.org/10.1155/2013/545636 |
| work_keys_str_mv | AT jinghaoli delaydependenthcontrolfordescriptormarkovianjumpsystemswithtimevaryingdelay AT qinglingzhang delaydependenthcontrolfordescriptormarkovianjumpsystemswithtimevaryingdelay AT dingzhai delaydependenthcontrolfordescriptormarkovianjumpsystemswithtimevaryingdelay AT yizhang delaydependenthcontrolfordescriptormarkovianjumpsystemswithtimevaryingdelay |