<i>H</i><sub>2</sub>state feedback controller design for continuous Markov jump linear systems with partly known information

Shen, Mouquan; Yang, Guang‐Hong

doi:10.1080/00207721.2010.523799

Cited by 34 publications

(39 citation statements)

References 24 publications

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“…Although partly known transition probabilities cover the cases of know, unknown with known bounds and completely unknown, the conditions given in [37] are conservative, which has been proved in [29]. In Theorem 1, by employing the transition probability matrix property (2) for continuous MJLS, there is no such scaling.…”

Section: Remarkmentioning

confidence: 96%

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New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities

Shen

Yang

2012

IET Control Theory &Amp; Applications

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In this study, the stability analysis and synthesis problems for continuous Markov jump linear systems with partly known transition probabilities are investigated. The partly known transition probabilities cover the cases that some elements are known, some are unknown with known lower and upper bounds and some are completely unknown. By making full use of the continuous transition probability matrix property, that is, the sum of transition probabilities is 0 for each row, a new method for the analysis and synthesis is presented in terms of solvability of a set of linear matrix inequalities. Compared to the existing results in the literature, it is shown that the proposed method is more effective to deal with the considered transition probabilities. Numerical examples are given to show the validity of the proposed method.

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Section: Remarkmentioning

confidence: 96%

“…Using scaling technology, the H 2 controller design problem for continuous MJLSs is solved in [37]. Although partly known transition probabilities cover the cases of know, unknown with known bounds and completely unknown, the conditions given in [37] are conservative, which has been proved in [29].…”

Section: Remarkmentioning

confidence: 99%

New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities

Shen

Yang

2012

IET Control Theory &Amp; Applications

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“…Thus, it leads to another interesting topic concerning MJ system, i.e., analysis and design for MJ system with partially unknown transition probabilities (TPs). For MJ system with partially unknown TPs, many important results have been established [18,19,20,21,22]. [18] studied the stability and stabilization problem for MJ system with partially unknown TPs, and [19] improved the results of [18].…”

Section: Introductionmentioning

confidence: 99%

“…When the capacity of the actuator is limited, [21] designed the bounded controller for MJ system subject to incomplete knowledge of TPs. [22] addressed the H 2 control problem for MJ system with partially unknown TPs. These works herein are all focused on the MJ differential equation, the research for MJ DI is rarely reported.…”

Section: Introductionmentioning

confidence: 99%

Stochastic observer design for Markovian jump Lur'e differential inclusion system

Huang

Sun

2014

The 26th Chinese Control and Decision Conference (2014 CCDC)

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This paper deals with the observer design for the Lur'e differential inclusion system with Markovian jump parameters. The information of transition probabilities is partially unknown. The stochastic observer is designed to make the error system exponentially stable in mean square. The condition for the existence of the stochastic observer is given by a set of linear matrix inequalities and linear matrix equalities. Finally, the rotor system is simulated to show the effectiveness of the proposed observer.

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“…The case has been addressed by [2], but its method cannot be used to deal with the case where there is no information available for transition probabilities. In [14], the 2 control problem for MJLS with more general partly known transition probabilities are investigated, which covers the cases that the transition probabilities are exactly known, completely unknown, and unknown but with known bounds. However, a conservative condition to relax inequality is used to derive the main result.…”

Section: Introductionmentioning

confidence: 99%

Improved H<inf>2</inf> controller design for Markov jump linear system with general transition probabilities

Fan

Zhao

2012

2012 12th International Conference on Control Automation Robotics &Amp; Vision (ICARCV)

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This paper concentrates on the problem of designing 2 state-feedback controllers for continuous-time Markovian jump linear systems (MJLSs) with more general transition rates. The elements in the considered transition rates matrix include completely known, boundary known and completely unknown ones. Some new techniques are proposed to deal with transition probabilities, and less conservative conditions than those in [14] for 2 performance analysis of MJLs are obtained in the framework of linear matrix inequalities. Moreover, the unknown transition probabilities can be decoupled from the Lyapunov matrices. As a result, new sufficient conditions for 2 controller vis state feedback are proposed. Finally, a numerical example is given to verify the effectiveness and superiority of the proposed method.

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H₂state feedback controller design for continuous Markov jump linear systems with partly known information

Cited by 34 publications

References 24 publications

New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities

New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities

Stochastic observer design for Markovian jump Lur'e differential inclusion system

Improved H<inf>2</inf> controller design for Markov jump linear system with general transition probabilities

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H2state feedback controller design for continuous Markov jump linear systems with partly known information

Cited by 34 publications

References 24 publications

New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities

New analysis and synthesis conditions for continuous Markov jump linear systems with partly known transition probabilities

Stochastic observer design for Markovian jump Lur'e differential inclusion system

Improved H<inf>2</inf> controller design for Markov jump linear system with general transition probabilities

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H₂state feedback controller design for continuous Markov jump linear systems with partly known information