Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates
•A new control problem for discrete singular Markov system is investigated.•Lyapunov function method, LMI technique and convex optimization are used.•Both actuator saturation and partly unknown transition rates are considered.•The derived conditions are less conservative have wider application range...
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| Published in | Applied Mathematical Modelling Vol. 53; pp. 49 - 70 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
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Elsevier Inc
01.01.2018
Elsevier BV |
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| Abstract | •A new control problem for discrete singular Markov system is investigated.•Lyapunov function method, LMI technique and convex optimization are used.•Both actuator saturation and partly unknown transition rates are considered.•The derived conditions are less conservative have wider application range.
In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov–Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods. |
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| AbstractList | In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov-Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods. •A new control problem for discrete singular Markov system is investigated.•Lyapunov function method, LMI technique and convex optimization are used.•Both actuator saturation and partly unknown transition rates are considered.•The derived conditions are less conservative have wider application range. In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and partly unknown transition rates. By constructing a proper Lyapunov–Krasonski functional and the method of linear matrix inequalities (LMIs), sufficient conditions that ensure the systems singular stochastic finite-time stability and singular stochastic finite-time dissipative are obtained. Then, the state feedback controllers are designed, and in order to get the optimal values of the dissipative level, the results are extended to LMI convex optimization problems. Finally, numerical examples are given to illustrate the validity of the proposed methods. |
| Author | Ma, Yuechao Liu, Deyou Jia, Xiaorui |
| Author_xml | – sequence: 1 givenname: Yuechao surname: Ma fullname: Ma, Yuechao – sequence: 2 givenname: Xiaorui orcidid: 0000-0002-5361-9689 surname: Jia fullname: Jia, Xiaorui email: jxfjia@163.com – sequence: 3 givenname: Deyou surname: Liu fullname: Liu, Deyou |
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| Keywords | Finite-time dissipative control Linear matrix inequality Actuator saturation Discrete-time singular system Partly unknown transition rates |
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| Snippet | •A new control problem for discrete singular Markov system is investigated.•Lyapunov function method, LMI technique and convex optimization are used.•Both... In this work, the finite-time dissipative control problem is considered for singular discrete-time Markovian jumping systems with actuator saturation and... |
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| SubjectTerms | Actuator saturation Controllers Convexity Discrete time systems Discrete-time singular system Dissipation Feedback control Finite-time dissipative control Jumping Linear matrix inequalities Linear matrix inequality Markov analysis Markov processes Mathematical analysis Matrix methods Optimization Partly unknown transition rates Saturation State feedback Stochastic models |
| Title | Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates |
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