Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach
This paper is concerned with the stochastic stability problem for discrete-time Markovian jump systems (DTMJSs) with time-varying delays. Two cases are discussed in the main results. On the one hand, it is assumed that the transition probability can be known. In this case, by constructing the Lyapun...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2017-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8115135/ |
| _version_ | 1819162525216800768 |
|---|---|
| author | Xin Li Xian Zhang Xin Wang |
| author_facet | Xin Li Xian Zhang Xin Wang |
| author_sort | Xin Li |
| collection | DOAJ |
| description | This paper is concerned with the stochastic stability problem for discrete-time Markovian jump systems (DTMJSs) with time-varying delays. Two cases are discussed in the main results. On the one hand, it is assumed that the transition probability can be known. In this case, by constructing the Lyapunov-Krasovskii functional and using some summation inequalities to estimate its forward difference, a new stochastic stability criterion of DTMJSs can be obtained, which has less conservatism than existing results. On the other hand, by utilizing the homogeneous polynomial approach, the novel delay-dependent stability condition of DTMJSs with uncertain transition probability is proposed. Finally, the results of numerical simulations demonstrate the effectiveness of the proposed methods. |
| first_indexed | 2024-12-22T17:29:37Z |
| format | Article |
| id | doaj.art-44f44024c26f4f3fb4629ada4e6d2f1b |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-22T17:29:37Z |
| publishDate | 2017-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-44f44024c26f4f3fb4629ada4e6d2f1b2022-12-21T18:18:40ZengIEEEIEEE Access2169-35362017-01-015275732758110.1109/ACCESS.2017.27756068115135Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial ApproachXin Li0Xian Zhang1https://orcid.org/0000-0001-7023-7351Xin Wang2School of Mathematical Science, Heilongjiang University, Harbin, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin, ChinaSchool of Mathematical Science, Heilongjiang University, Harbin, ChinaThis paper is concerned with the stochastic stability problem for discrete-time Markovian jump systems (DTMJSs) with time-varying delays. Two cases are discussed in the main results. On the one hand, it is assumed that the transition probability can be known. In this case, by constructing the Lyapunov-Krasovskii functional and using some summation inequalities to estimate its forward difference, a new stochastic stability criterion of DTMJSs can be obtained, which has less conservatism than existing results. On the other hand, by utilizing the homogeneous polynomial approach, the novel delay-dependent stability condition of DTMJSs with uncertain transition probability is proposed. Finally, the results of numerical simulations demonstrate the effectiveness of the proposed methods.https://ieeexplore.ieee.org/document/8115135/Discrete time-delay Markovian jump systemsstochastic stabilityhomogeneous polynomial approachuncertain transition probability |
| spellingShingle | Xin Li Xian Zhang Xin Wang Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach IEEE Access Discrete time-delay Markovian jump systems stochastic stability homogeneous polynomial approach uncertain transition probability |
| title | Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach |
| title_full | Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach |
| title_fullStr | Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach |
| title_full_unstemmed | Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach |
| title_short | Stability Analysis for Discrete-Time Markovian Jump Systems With Time-Varying Delay: A Homogeneous Polynomial Approach |
| title_sort | stability analysis for discrete time markovian jump systems with time varying delay a homogeneous polynomial approach |
| topic | Discrete time-delay Markovian jump systems stochastic stability homogeneous polynomial approach uncertain transition probability |
| url | https://ieeexplore.ieee.org/document/8115135/ |
| work_keys_str_mv | AT xinli stabilityanalysisfordiscretetimemarkovianjumpsystemswithtimevaryingdelayahomogeneouspolynomialapproach AT xianzhang stabilityanalysisfordiscretetimemarkovianjumpsystemswithtimevaryingdelayahomogeneouspolynomialapproach AT xinwang stabilityanalysisfordiscretetimemarkovianjumpsystemswithtimevaryingdelayahomogeneouspolynomialapproach |