Exponential stability analysis for a class of neutral singular Markovian jump systems with time-varying delays

Long, Siyu; Zhong, Shouming; Guan, Hongbo; Zhang, Dian

doi:10.1016/j.jfranklin.2019.04.036

Cited by 20 publications

(12 citation statements)

References 31 publications

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“…, and Π 2 , are defined in Appendix A. en, the reachable sets of system (1) with (2) and (3) are bounded by boundaries ∩ N i�1 I(P 1,i ), which is defined in (12).…”

Section: Journal Of Mathematicsmentioning

confidence: 99%

“…where (1) 44 � − 9R 6 e − αh 2 , π (1) 46 � 3R 6 e − αh 2 , π (1) 4,10 � − 24R 6 e − αh 2 , π (1) 4,12 � 60R 6 e − αh 2 , π (1) 66 � − 9R 6 e − αh 2 , π (1) 6,10 � 36R 6 e − αh 2 , π (1) 6,12 � − 60R 6 e − αh 2 , π (1) 10,10 � − 192R 6 e − αh 2 , π (1) 10,12 � 360R 6 e − αh 2 , π (1) 12,12 � − 720R 6 e − αh 2 , π (2) 44 � − 9R 6 e − αh 2 , π (2) 45 � 3R 6 e − αh 2 , π (2) 4,11 � − 24R 6 e − αh 2 , π (2) 4,13 � 60R 6 e − αh 2 , π (1) 55 � − 9R 6 e − αh 2 , π (2) 5,11 � 36R 6 e − αh 2 , π (2) 5,13 � − 60R 6 e − αh 2 , π (2) 11,11 � − 192R 6 e − αh 2 , π (2) 11,13 � 360R 6 e − αh 2 , π (2) 13,13 � − 720R 6 e − αh 2 , π (3) 44 � e − αh 2 sym Y 11 + sym…”

Section: Journal Of Mathematics 23unclassified

“…Markovian jump systems, modeled by a set of subsystems with transitions among the models determined by a Markov chain taking values in a finite set, have appealed to a lot of researchers in the control community. In the past few decades, the Markovian jump systems have been extensively studied (see [1][2][3] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

“…60R 5 e − αh m , ϕ(2) 11,11 � − 192R 5 e − αh m , ϕ(2) 11,13 � 360R 5 e − αh m , ϕ(2) 13,13 � − 720R 5 e − αh m , − αh m sym X 11 + sym X 21 + sym X 31 − sym X 12 − sym X 22 − sym X 32 + sym X 13 + sym X 23 + sym X 33 ,…”

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Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

Zhou

Shen

et al. 2021

Journal of Mathematics

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In this paper, we are concerned with the problem of reachable set estimation for uncertain Markovian jump systems with time-varying delays and disturbances. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set of Markovian jump system as small as possible. Based on an augmented Lyapunov–Krasovskii functional, by dividing the time-varying delay into two nonuniform subintervals, more general delay-dependent stability criteria for the existence of a desired ellipsoid are derived. An optimized integral inequality which is based on distinguished Wirtinger integral inequality and reciprocally convex combination inequality is used to deal with the integral terms. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

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“…, and Π 2 , are defined in Appendix A. en, the reachable sets of system (1) with (2) and (3) are bounded by boundaries ∩ N i�1 I(P 1,i ), which is defined in (12).…”

Section: Journal Of Mathematicsmentioning

confidence: 99%

Section: Journal Of Mathematics 23unclassified

Section: Introductionmentioning

confidence: 99%

unclassified

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Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

Zhou

Shen

et al. 2021

Journal of Mathematics

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“…Motivated by some ideas and methods in [16,[32][33][34][35][36][37][38][39][40]46], we are to investigate the stability of a class of p-Laplacian diffusion T-S fuzzy system via variational methods that are different from those of existing literature related to reaction-diffusion fuzzy systems.…”

Section: Introductionmentioning

confidence: 99%

pth Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

2020

Self Cite

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In this paper, the Sobolev embedding theorem, Holder inequality, the Lebesgue contrl convergence theorem, the operator norm estimation technique, and critical point theory are employed to prove the existence of nontrivial stationary solution for p-Laplacian diffusion system with distributed delays. Furthermore, by giving the definition of pth moment stability, the authors use the Lyapunovfunctional method and Kamke function to derive the stability of nontrivialstationary solution. Moreover, a numerical example illuminates the effectiveness of the proposed methods. Finally, an interesting further thought is put forward, which is conducive to the in-depth study of the problem.

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Further analysis of stabilization of neutral type singular systems with mixed time‐varying delays and multiple random states

Yi,

Lu,

Wang

2024

Asian Journal of Control

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In this paper, the stabilization problem of neutral type singular systems (NTSSs) with mixed time‐varying delays and multiple random states is further analyzed. Lyapunov Krasovskill functional (LKF) and generalized Itô formula, together with linear matrix inequality (LMI), are used to represent a new stability criterion for NTSSs with mixed time‐varying delays (MTVDs) in multiple random states. First, the regularity, impulse free, and stochastic stability of the system are satisfied by designing a state feedback controller (SFC). Second, on the basis of Leibniz Newton formula, the stability criterion is also feasible by integrating zero value equation technology, and then combined with singular decomposition, the gain of SFC is obtained. Finally, our paper is a further analysis of the latest literature, so two numerical examples are used to verify the feasibility and effectiveness of this method.

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Exponential stability analysis for a class of neutral singular Markovian jump systems with time-varying delays

Cited by 20 publications

References 31 publications

Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

Reachable Set Estimation for Uncertain Markovian Jump Systems with Time-Varying Delay and Disturbances

pth Moment Stability of a Stationary Solution for a Reaction Diffusion System with Distributed Delays

Further analysis of stabilization of neutral type singular systems with mixed time‐varying delays and multiple random states

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