Controllability on a class of switched time-varying systems with impulses and multiple time delays

Zhang, Ding-Xue; Yan, Jiayuan; Hu, Bin; Guan, Zhi‐Hong; Zheng, Ding-Fu

doi:10.1080/00207721.2022.2050436

Cited by 5 publications

(2 citation statements)

References 40 publications

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“…Liu et al [12,13] studied the multi-cluster behaviors of a specific Motsch-Tadmor system with processing time delay and cut-off weights. For more delayed collective systems, see previous studies [14][15][16][17][18][19][20][21][22][23][24][25]. All results imply that whether the adjacency matrix is connected and whether there is a time delay significantly impacts the dynamic behaviors of the multi-particle systems.…”

Section: Introductionsupporting

confidence: 54%

Asymptotic collective behaviors of a delayed multi‐particle system with multiple processes

Liu,

Liu

2023

Math Methods in App Sciences

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It is a significant issue to explore the collective behaviors of the delayed complex systems. This paper studies asymptotic collective behaviors of a delayed multi‐particle system with multiple processes while particles interact directionally and locally. Up to now, the studies on dynamic behaviors of multi‐particle systems do not involve limited processing capacity, that is, the information queuing phenomenon is ignored. To this aim, we introduce multiple processes to formulate the evolution of a delayed multi‐particle system. To optimize the delay parameters, we choose the greedy principle to set the processing order. The main idea is to decompose the velocity into each process and use functional differential equation theory and matrix theory to constrain the velocity variation rate while the processing order is fixed. As the new results, in the non‐critical and general situation, when the time delay is less than or equal to the threshold value and the eigenvalue 1 of the average matrix is semi‐simple, we achieve the criterion of flocking and multi‐cluster with exponential convergence rate involving multiple processes. Furthermore, we get the lower bound estimate of the processing capacity.

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Section: Introductionsupporting

confidence: 54%

Asymptotic collective behaviors of a delayed multi‐particle system with multiple processes

Liu,

Liu

2023

Math Methods in App Sciences

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“…In [23], the authors investigate linear switched systems and propose several necessary and sufficient conditions by using the invariant subspace to describe a controllable set. [24,25] derive several sufficient conditions for impulsive switched systems by virtue of Gramian matrices. [26] discusses local controllability of affine systems by employing the Lie algebraic method.…”

Section: Introductionmentioning

confidence: 99%

Relative controllability of nonlinear switched fractional systems

Luo,

Liu,

Zhao

et al. 2023

Asian Journal of Control

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This article investigates relative controllability of nonlinear switched fractional systems (SFSs). With the aid of Mittag‐Leffler functions and invariant subspace theory, two sufficient and necessary conditions for corresponding linear SFSs are first established. Then, piecewise continuous control functions and a novel nonlinear operator are constructed to overcome the difficulties arising from switching rules, nonlinearity, and fractional derivatives. Under different constraints on nonlinear functions, two controllability conditions depending on system parameters for nonlinear SFSs are proposed by applying Schauder's and Banach's fixed point theorems, respectively. The obtained criteria may well show the influence of coefficient matrices, fractional derivatives, and switching rules on relative controllability. In addition, our proposed method is also applicable for integer‐order switched systems. Finally, two simulated examples are worked out to verify the theoretical results.

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Finite time stability of neutral multiterm fractional order time-varying delay systems

Kaliraj,

Priya,

Tamilarasan

et al. 2025

Journal of Computational and Applied Mathematics

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Controllability on a class of switched time-varying systems with impulses and multiple time delays

Cited by 5 publications

References 40 publications

Asymptotic collective behaviors of a delayed multi‐particle system with multiple processes

Asymptotic collective behaviors of a delayed multi‐particle system with multiple processes

Relative controllability of nonlinear switched fractional systems

Finite time stability of neutral multiterm fractional order time-varying delay systems

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