Finite‐time stability of non‐linear systems with impulsive effects due to logic choice

Zhang, Junhui; Wang, Qing‐Guo

doi:10.1049/iet-cta.2017.0886

Cited by 12 publications

(9 citation statements)

References 33 publications

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“…Step 2: From M we know that there are 165 columns greater than or equal to 1 n in M and can get the following set K . {1, 2, 3,4,5,6,7,8,9,10,11,13,14,15,17,18,19,20,21,22,23,24,25,26,27,29,30,31,33,34,35,36,37,38,39,40,41,42,43,45,46,47 174,177,178,179,180,181,182,185,187,189,193,194,195,196,197,198,201,…”

Section: The Unitary Adjacency Matrix Ofmentioning

confidence: 99%

Algebraic Expression and Construction of Control Sets of Graphs Using Semi-Tensor Product of Matrices

et al. 2019

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Using a new matrix analysis tool, called semi-tensor product of matrices (STP) developed in recent years, this paper investigates the problem of finding control sets (or dominating sets) of graphs mathematically. By defining characteristic vectors for vertex subsets of graphs, three sufficient and necessary conditions of control sets are proposed, based on which an algebraic algorithm that can find all the control sets of a graph is established. Further, the concepts of k-capacity and k-harmony control sets of graphs are proposed, which can model some real-world problems such as security monitoring of streets and wireless sensor networks. Several sufficient and necessary conditions are established to judge whether or not a vertex subset is a k-capacity control set; a necessity that a vertex subset is a k-harmony control set is proposed, which facilitates finding all the k-harmony control sets of graphs. The correctness and effectiveness of the results is finally examined in detail by examples. The approach of this paper may provide a new angle and means to understand and analyze the structure of graphs.INDEX TERMS Algebraic approach, finite-valued systems, graphs, logical dynamical systems, logical systems, semi-tensor product of matrices.

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Section: The Unitary Adjacency Matrix Ofmentioning

confidence: 99%

Algebraic Expression and Construction of Control Sets of Graphs Using Semi-Tensor Product of Matrices

et al. 2019

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“…For example, dynamic walking of biped robots is well researched by impulsive system (see [18,19]), some stable characteristics of biped robots can be achieved by imposing some logic choice on the impulses. Therefore, an interesting recent development of the impulsive system is the logic impulses (see [20][21][22]), that is the impulsive effects are suffered by logic choice which was firstly established in [20].…”

Section: Introductionmentioning

confidence: 99%

“…The main results of this paper can be concluded as follows: (i) the author constructs a class of linear stochastic delay differential system with variable impulses due to logic choice, in which the logic impulses generalize the logic impulses established in [20] and [21]; (ii) its stabilities are equivalent respectively to the stabilities of a corresponding SD, if some desired conditions are satisfied. It's worth noting that, by establishing the equivalent relation between the solutions of SDLI and SD, it is able to overcome the Itô's formula application difficulty mentioned above that the impulses lie in the integrating intervals; (iii) the application of theorem results in a class of linear stochastic delay differential systems with logic impulses is discussed.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, the stability of stochastic delay differential systems with variable impulses due to logic choice has been investigated. Firstly, the author has introduced a class of linear stochastic delay differential system with variable impulses due to logic choice, in which the logic impulses generalize the logic impulses established in [20] and [21]. Then, by establishing the equivalent relation between the solutions of SDLI and SD, some stability criteria for SDLI and SD have been proposed.…”

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Stability of Stochastic Delay Differential Systems With Variable Impulses Due to Logic Choice

2021

IEEE Access

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This paper is concerned with stability problems of stochastic delay differential systems with variable impulses due to logic choice. Firstly, a class of variable impulses due to logic choice is introduced in this paper which is more general than the logic impulses established in [20] and [21]. Then, by establishing a connection between the stochastic delay differential system with logic impulses and a corresponding stochastic delay differential system without logic impulses, some sufficient conditions for stability of the systems are obtained. Finally, the application in a class of linear stochastic delay differential systems with logic impulses is discussed, and several stability criteria together with two numerical examples are given.

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“…For the robust distributed MPC (DMPC), it is motivated by dynamically decoupled agents, which need to achieve some coordination and perform a cooperation task through a distributed manner in actual industry [4][5][6]. For such networked control systems, the constraints include not only the conventional time-triggered constraints, such as state constraints at sampling times but also communication constraints, such as the limited bandwidth when transmitting data by using wireless networks [7][8][9][10][11]. This wireless transmission can reduce the cabling and communication infrastructure cost to a certain extent.…”

Section: Introductionmentioning

confidence: 99%

Robust event‐triggered distributed min–max model predictive control of continuous‐time non‐linear systems

2020

IET Control Theory & Appl

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Due to the features of event-triggered control in exploiting and saving system resources, they have been widely applied in sensor networks, multi-agent systems, networked control systems and so on. In this study, the authors focused on robust event-triggered distributed model predictive control (RETDMPC). Subject to disturbances and parametric uncertainties, they first applied the min-max model to RETDMPC. The min-max RETDMPC methodology is used to guarantee the robustness of the system state by taking the worst possible case of unknown uncertainties into consideration. Furthermore, in this framework, a new cost function is developed in which unknown uncertainties are considered. Next, sufficient conditions are provided to ensure the feasibility and stability of their developed min-max RETDMPC. Finally, a practical example is given to illustrate the advantages of their algorithm by comparing to the conventional model predictive control.

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Finite‐time stability of non‐linear systems with impulsive effects due to logic choice

Cited by 12 publications

References 33 publications

Algebraic Expression and Construction of Control Sets of Graphs Using Semi-Tensor Product of Matrices

Algebraic Expression and Construction of Control Sets of Graphs Using Semi-Tensor Product of Matrices

Stability of Stochastic Delay Differential Systems With Variable Impulses Due to Logic Choice

Robust event‐triggered distributed min–max model predictive control of continuous‐time non‐linear systems

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