Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities
This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties th...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2021-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9333568/ |
| _version_ | 1818734527654133760 |
|---|---|
| author | Yuan Li Zhongxin Yu Yang Liu Junchao Ren |
| author_facet | Yuan Li Zhongxin Yu Yang Liu Junchao Ren |
| author_sort | Yuan Li |
| collection | DOAJ |
| description | This paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities (LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less. |
| first_indexed | 2024-12-18T00:06:47Z |
| format | Article |
| id | doaj.art-ece4786dca0045fca6e64cd023b24c55 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-18T00:06:47Z |
| publishDate | 2021-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-ece4786dca0045fca6e64cd023b24c552022-12-21T21:27:47ZengIEEEIEEE Access2169-35362021-01-019269372694710.1109/ACCESS.2021.30538659333568Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition ProbabilitiesYuan Li0https://orcid.org/0000-0001-7993-0611Zhongxin Yu1https://orcid.org/0000-0002-1845-8090Yang Liu2https://orcid.org/0000-0003-0692-2578Junchao Ren3https://orcid.org/0000-0002-9766-1758School of Science, Shenyang University of Technology, Shenyang, ChinaSchool of Science, Shenyang University of Technology, Shenyang, ChinaSchool of Electrical Engineering, Shenyang University of Technology, Shenyang, ChinaCollege of Science, Northeastern University, Shenyang, ChinaThis paper investigates the problem of state feedback controller design for discrete-time Markovian jump systems (MJSs) with time delay and two Markov chains under partly known transition probabilities. First, by constructing improved Lyapunov-Krasovskii functional (LKF), utilizing the properties that the sum of each row is one in a transition probability matrix and some tractable linear matrix inequalities (LMI), a sufficient condition is established such that the system under consideration is stochastically stable. Second, the design method of time-delay-dependent state feedback controller is proposed to ensure that the resulting closed-loop system is stochastically stable. Since no free matrix variables are applied under the proposed conditions, the method proposed reduce the complexity of calculations. Finally, two simulation examples are presented to show the effectiveness of the proposed method. Compared with the existing literature, in the proposed method not only the conservatism is reduced under the derived stability and stabilization conditions, but also the total number of matrix inequalities is less.https://ieeexplore.ieee.org/document/9333568/Markovian jump systemsMarkov chainsstochastic stabilitytransition probabilities |
| spellingShingle | Yuan Li Zhongxin Yu Yang Liu Junchao Ren Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities IEEE Access Markovian jump systems Markov chains stochastic stability transition probabilities |
| title | Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities |
| title_full | Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities |
| title_fullStr | Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities |
| title_full_unstemmed | Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities |
| title_short | Stochastic Stabilization for Discrete-Time Markovian Jump Systems With Time-Varying Delay and Two Markov Chains Under Partly Known Transition Probabilities |
| title_sort | stochastic stabilization for discrete time markovian jump systems with time varying delay and two markov chains under partly known transition probabilities |
| topic | Markovian jump systems Markov chains stochastic stability transition probabilities |
| url | https://ieeexplore.ieee.org/document/9333568/ |
| work_keys_str_mv | AT yuanli stochasticstabilizationfordiscretetimemarkovianjumpsystemswithtimevaryingdelayandtwomarkovchainsunderpartlyknowntransitionprobabilities AT zhongxinyu stochasticstabilizationfordiscretetimemarkovianjumpsystemswithtimevaryingdelayandtwomarkovchainsunderpartlyknowntransitionprobabilities AT yangliu stochasticstabilizationfordiscretetimemarkovianjumpsystemswithtimevaryingdelayandtwomarkovchainsunderpartlyknowntransitionprobabilities AT junchaoren stochasticstabilizationfordiscretetimemarkovianjumpsystemswithtimevaryingdelayandtwomarkovchainsunderpartlyknowntransitionprobabilities |