Stochastic stability and stabilization of Markov jump linear systems with instantly time-varying transition rates: A unified framework

Niri, Mona Faraji; Jahed‐Motlagh, Mohammad Reza

doi:10.1016/j.isatra.2016.06.011

Cited by 18 publications

(7 citation statements)

References 27 publications

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“…From condition (14), it is concluded that G is nonsingular. Meanwhile, under the condition (30), it is obvious that the condition (14) with the (18) can imply the (29). At the same time, it is easy to notice that ( 26) can be guaranteed by (15).…”

Section: Resultsmentioning

confidence: 97%

“…Example 1: In order to prove the effectiveness and applicability of the developed theoretical results, we consider a single-machine infinite-bus (SMIB) power system, which is cited from [29]. For convenience, it is seen that some unnecessary factors are ignored during the process of modeling the SMIB power system, such as the stator winding resistance, voltages due to magnetic flux derivatives, damper windings and so on.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Observer-Based Controller Design for Discrete-Time Markovian Jump Linear Systems With Partial Information

Liu

Wang

2019

IEEE Access

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In this paper, the observer-based controller problem is considered for a class of discretetime Markovian jump systems with partial information. We consider the situation that the parameters on Markov chain discussed in this paper may not be totally observed, which is different from the traditional case with complete information on Markov parameters. First, although the operating modes are not completely available, one kind of detector submitting the information on operating modes is provided. Then, a kind of observer and an observer-based controller are constructed in order to achieve the observation of system state and assure the stabilization of the closed-loop systems, respectively. At the same time, sufficient conditions on the existence of the observer and the corresponding controller are presented in terms of linear matrix inequalities (LMIs). Finally, the simulations illustrate the advantage and potential application of the proposed theoretical results.INDEX TERMS Markovian jump systems, observer-based controller, partial information, linear matrix inequalities (LMIs).

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Section: Resultsmentioning

confidence: 97%

Section: Resultsmentioning

confidence: 99%

Observer-Based Controller Design for Discrete-Time Markovian Jump Linear Systems With Partial Information

Liu

Wang

2019

IEEE Access

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“…Example Consider system (1) whose matrices are partially cited from Reference 40 and described to be

\begin{matrix} A_{1} & = ([], \begin{matrix} subarray \\ array - 0.8 + δ & array 1 & array 0 \\ array 0 & array - 0.26 & array - 1.2 \\ array 0 & array 1.2 & array - 0.42 \end{matrix}), A_{2} = ([], \begin{matrix} subarray \\ array - 0.1 & array 1 & array 0 \\ array 0 & array - 0.6 & array - 2.2 \\ array 0 & array 0.5 & array - 1.4 \end{matrix}), \\ B_{1} & = ([], \begin{matrix} subarray \\ array - 0.12 & array 0.15 & array 0.13 \\ array 0.11 & array 0.32 & array - 0.23 \\ array 0.016 & array - 0.045 & array 0.32 \end{matrix}), B_{2} = ([], \begin{matrix} subarray \\ array 0.17 & array - 0.018 & array 0.43 \\ array - 0.06 & array 0.23 & array - 0.13 \\ array 0.032 & array 0.32 & array 0.53 \end{matrix}), \end{matrix}

where parameter

δ \geq 0

added to matrix

A_{1}

is denoted as an uncertainty and used to make some comparisons. It is seen that there are two modes such as

η (t) \in N = {1, 2}

, and its transition probability matrix is given as

…”

Section: Numerical Examplementioning

confidence: 99%

Stability analysis of delayed Markovian jump systems with delay switching and state signals and applications

Wang

Ren

2022

Intl J Robust & Nonlinear

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This article addresses the asymptotical mean square stability problem of continuous-time delayed Markovian jump systems (MJSs). Different from the existing delayed MJS models, time-varying delays are contained in not only system state but also switching signal and could lead to great difficulties. An auxiliary system approach is developed to handle the difficulties, in which the traditionally delayed state and a new delayed exponential matrix are both involved. Based on the established model, sufficient stability conditions with solvable forms are given by using a Lyapunov function approach and some novel techniques. More extensions about an MJS under sampled switching and state signals are further considered, and so does the stabilization problem. A numerical example is offered to verify the effectiveness and superiority of the methods proposed in this study.

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“…Another Markov process, which governs the transition between different finite transition rates of previous Markov processes (low-level Markov signals), is called a high-level Markov signal. Stability problems for neural networks and linear systems with inhomogeneous Markovian parameters have been investigated based on the linear matrix inequality approach (Faraji-Niri and Jahed-Motlagh, 2016; Faraji-Niri et al, 2017; Wu et al, 2012a; Zhang, 2009). Wu et al (2012a) analysed the stability problem of piecewise homogeneous Markovian jump neural networks with both discrete and distributed delays by utilizing the linear matrix inequality method.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of H ∞ control for piecewise homogeneous Markovian jump linear systems has been investigated by Zhang (2009). Faraji-Niri and Jahed-Motlagh (2016) studied a class of inhomogeneous Markov jump linear systems with instantly time-varying transition rates. In addition, the stochastic stability and stabilization problem of uncertain continuous-time Markov jump linear systems with piecewise-constant time-varying transition rates has been solved by Faraji-Niri et al (2017).…”

Section: Introductionmentioning

confidence: 99%

Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay

Akbari

Sadr

Kazemy

2018

Transactions of the Institute of Measurement and Control

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The exponential synchronization of a Markovian jump complex dynamical network with piecewise-constant transition rates is investigated. Two distinct types of time-varying delay are considered for the system; one is distributed time-delay for each node, the other is discrete coupling time-delay. Based on an augmented Lyapunov–Krasovskii functional, some sufficient conditions are derived and expressed in the form of linear matrix inequalities, which are formulated in such a manner as to determine the controller gain matrices. Finally, an example is given to illustrate the effectiveness and validity of the proposed method.

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Stochastic stability and stabilization of Markov jump linear systems with instantly time-varying transition rates: A unified framework

Cited by 18 publications

References 27 publications

Observer-Based Controller Design for Discrete-Time Markovian Jump Linear Systems With Partial Information

Observer-Based Controller Design for Discrete-Time Markovian Jump Linear Systems With Partial Information

Stability analysis of delayed Markovian jump systems with delay switching and state signals and applications

Exponential synchronization of a Markovian jump complex dynamic network with piecewise-constant transition rates and distributed delay

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