Reachable set synthesis of singular Markovian jump systems

Feng, Zhiguang; Jiang, Zhengyi; Zheng, Wei Xing

doi:10.1016/j.jfranklin.2020.09.042

Cited by 27 publications

(4 citation statements)

References 24 publications

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“…This kind of desired control scheme has a strong robustness and anti-interference capability, which is necessary to guarantee the work safety for the target system with a combination of both theoretical and practical significance. Therefore, the issue of the RSS associated with different systems has attracted many attention of scholars in the past decades, such as neural network systems, 34,35 singular systems, 31,36 time-delay systems, 37,38 and switched systems. 39,40 Besides, the article 41 investigates the RSS issue of MJSs with time-varying delays subject to the hidden Markov model (HMM) and general transition probabilities.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the proposed dynamic stochastic system, an integral switching surface is established. In another work of Feng et al 31 studies the issue of reachable set synthesis (RSS) for singular MJSs based on proportional and derivative state feedback control and a practical example as application is used to verify the effectiveness of the proposed method. The disturbance attenuation and rejection issue for stochastic MJSs is considered in Reference 32.…”

Section: Introductionmentioning

confidence: 99%

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Hidden Markov model‐based approach on real‐time output reachable set synthesis for discrete‐time nonlinear Markovian jump systems

Feng

et al. 2023

Intl J Robust & Nonlinear

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This note addresses the asynchronous state-feedback control (ASC) for delay nonlinear Markovian jump systems (DNMJSs) subject to reachable set boundary. Under taking time-varying delays and external disturbance into consideration, Takagi-Sugeno fuzzy model is adopted to approximate the nonlinear dynamics systems. Although the assumption about time-delay is practical, it will cause subsystem modes to be not synchronous with the controller modes. As a consequence, the description method of the nonsynchronous phenomenon is introduced, which is a hidden Markov model. Furthermore, an available ASC is designed and all reachable states of the system is constrained within the compact ellipsoidal boundary to guarantee the safe operation of the DNMJSs. The existence conditions of the desired ASC are obtained via solving a group of feasible linear matrix inequalities. Finally, some numerical simulations are provided to verify the availability of the proposed method in this article.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hidden Markov model‐based approach on real‐time output reachable set synthesis for discrete‐time nonlinear Markovian jump systems

Feng

et al. 2023

Intl J Robust & Nonlinear

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“…Therefore, it can play a very positive role to study singular Markov jump systems theoretically and practically. Recently, it has been revealed that stability analysis, observer design, controller design, and various control methods of singular Markov jump systems have become the research hotspot [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Robust H∞ sliding mode control for uncertain discrete singular T‐S fuzzy Markov jump systems

Wang

Han

Gao

2022

Asian Journal of Control

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This paper mainly explored the problem of stability in terms of discrete singular T‐S fuzzy Markov jump systems with uncertainties and external disturbances. A new sliding mode controller is proposed for this type of system. Firstly, a common sliding surface that can be shared by all subsystems of discrete singular systems is designed, so the jumping effects could be weakened. Secondly, the proof of stochastic admissibility of the closed‐loop dynamic system is provided by deriving the linear matrix inequality (LMI) technique. Thirdly, an appropriate sliding mode control (SMC) law is designed to satisfy the discrete reaching condition. And, finally, a simulation is offered to illustrate the effectiveness of the derived results.

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“…For singular MJSs, sufficient and necessary conditions for stability and stabilization of continuous-time singular MJSs were given in [21], and the dynamic output feedback control for singular MJSs was given in [22] by using linear matrix inequality technology. When the system was subject to amplitude bounded disturbance, the PD state feedback control method was extended to the reachable set synthesis problem [23]. The dissipative control problem for T-S fuzzy singular MJSs was studied in [24], where the state-dependent noise and asynchronous modes were considered.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Control of Singular Linear Semi-Markov Jump Systems

Ji¹,

Liu²

2021

Algorithms

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The problem of finite-time control for singular linear semi-Markov jump systems (SMJSs) with unknown transition rates is considered in this paper. By designing a new semi-positive definite Lyapunov-like function, state feedback controller design methods are given that allow closed-loop singular linear SMJSs to be regular, impulse-free and stochastically finite-time-stable without external disturbance, and stochastically finite-time bounded with external disturbance. The obtained conditions are expressed by a set of strict matrix inequalities, which can be simplified to a set of linear matrix inequalities by a one dimensional search for a scalar. Two numerical examples are given to illustrate the effectiveness of proposed method.

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Reachable set synthesis of singular Markovian jump systems

Cited by 27 publications

References 24 publications

Hidden Markov model‐based approach on real‐time output reachable set synthesis for discrete‐time nonlinear Markovian jump systems

Hidden Markov model‐based approach on real‐time output reachable set synthesis for discrete‐time nonlinear Markovian jump systems

Robust H∞ sliding mode control for uncertain discrete singular T‐S fuzzy Markov jump systems

Finite-Time Control of Singular Linear Semi-Markov Jump Systems

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