Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays
Abstract This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov–Krasovskii functional, a set of new sufficient conditions...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-02-01
|
| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-1987-6 |
| _version_ | 1818272603996946432 |
|---|---|
| author | Nannan Ma Zhibin Liu Lin Chen |
| author_facet | Nannan Ma Zhibin Liu Lin Chen |
| author_sort | Nannan Ma |
| collection | DOAJ |
| description | Abstract This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov–Krasovskii functional, a set of new sufficient conditions is developed which not only guarantee the stochastic stability of the sliding-mode dynamics, but also satisfy the H∞ ${H_{\infty}}$ performance. Next, an integral sliding surface is designed to guarantee that the closed-loop error system reach the designed sliding surface in a finite time. Finally, an example is given to illustrate the validity of the obtained theoretical results. |
| first_indexed | 2024-12-12T21:44:42Z |
| format | Article |
| id | doaj.art-8ccb160c272d405c8177fb08ad6dbf8e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T21:44:42Z |
| publishDate | 2019-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-8ccb160c272d405c8177fb08ad6dbf8e2022-12-22T00:10:57ZengSpringerOpenAdvances in Difference Equations1687-18472019-02-012019111810.1186/s13662-019-1987-6Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delaysNannan Ma0Zhibin Liu1Lin Chen2School of Science, Southwest Petroleum UniversitySchool of Science, Southwest Petroleum UniversitySchool of Science, Southwest Petroleum UniversityAbstract This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov–Krasovskii functional, a set of new sufficient conditions is developed which not only guarantee the stochastic stability of the sliding-mode dynamics, but also satisfy the H∞ ${H_{\infty}}$ performance. Next, an integral sliding surface is designed to guarantee that the closed-loop error system reach the designed sliding surface in a finite time. Finally, an example is given to illustrate the validity of the obtained theoretical results.http://link.springer.com/article/10.1186/s13662-019-1987-6Complex dynamical networksSliding-mode controlMarkovian jump parametersH ∞ ${H_{\infty}}$ performance |
| spellingShingle | Nannan Ma Zhibin Liu Lin Chen Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays Advances in Difference Equations Complex dynamical networks Sliding-mode control Markovian jump parameters H ∞ ${H_{\infty}}$ performance |
| title | Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays |
| title_full | Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays |
| title_fullStr | Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays |
| title_full_unstemmed | Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays |
| title_short | Sliding-mode H∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays |
| title_sort | sliding mode h∞ h infty synchronization for complex dynamical network systems with markovian jump parameters and time varying delays |
| topic | Complex dynamical networks Sliding-mode control Markovian jump parameters H ∞ ${H_{\infty}}$ performance |
| url | http://link.springer.com/article/10.1186/s13662-019-1987-6 |
| work_keys_str_mv | AT nannanma slidingmodehhinftysynchronizationforcomplexdynamicalnetworksystemswithmarkovianjumpparametersandtimevaryingdelays AT zhibinliu slidingmodehhinftysynchronizationforcomplexdynamicalnetworksystemswithmarkovianjumpparametersandtimevaryingdelays AT linchen slidingmodehhinftysynchronizationforcomplexdynamicalnetworksystemswithmarkovianjumpparametersandtimevaryingdelays |