Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control

Rakkiyappan, R.; Sasirekha, R.; Shanmugam, Lakshmanan; Lim, Chee Peng

doi:10.1016/j.jfranklin.2016.07.024

Cited by 21 publications

(9 citation statements)

References 35 publications

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“…For this case, it is realistic to synthesize a controller for a given uncertain system such that the controller is insensitive to some predefined admissible variations with respect to its gains. More recently, many efforts have been devoted to the nonfragile robust H ∞ controller design problem [31][32][33][34][35][36][37][38][39][40]. For instance, a nonfragile H ∞ controller with multiplicative gain perturbations was proposed for linear time invariant (LTI) systems in [31].…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…T and = 1, the controller gains can be obtained as It is worth pointing out that when ≡ 0, the piecewise affine nonfragile controller (9) is characterized as a piecewise linear nonfragile controller given in (36). With = 1, Table 1 compares the robust performance between piecewise affine nonfragile controllers with piecewise linear nonfragile controllers with different matrix .…”

Section: Simulationmentioning

confidence: 99%

“…It can be seen from Figure 1(a) that the curves of system states converge to the zero after 20s. With the same initial conditions and external disturbance, use the piecewise linear nonfragile controller as in (36), and the time responses of the closed-loop system are demonstrated in Figures 2(a) and 2(b). Figure 2(a) shows that the curves of the closed-loop system states converge to the zero after 28s.…”

Section: Simulationmentioning

confidence: 99%

“…(b) Response of the ratio by using piecewise affine nonfragile controller(36) Response of the ratio √ ∫ 0 T ( ) ( ) / √ ∫ 0 T ( ) ( ) in Example 1.…”

mentioning

confidence: 99%

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A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

Chen

Pang

Zhao

et al. 2018

Mathematical Problems in Engineering

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This paper investigates the robust H∞ nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust H∞ performance γ. By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

“…(b) Response of the ratio by using piecewise affine nonfragile controller(36) Response of the ratio √ ∫ 0 T ( ) ( ) / √ ∫ 0 T ( ) ( ) in Example 1.…”

mentioning

confidence: 99%

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A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

Chen

Pang

Zhao

et al. 2018

Mathematical Problems in Engineering

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“…In recent research of complex network, most of them are about static characteristics, chaos control of complex network. The research on static characteristics is mainly concentrating on some classic statistical characteristic and their applications [5][6][7], and the analysis of network chaos control is mainly involved in chaos synchronization and the method of improving network synchronizability [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

A New Complex Network Model with Multiweights and Its Synchronization Control

Zhang²

2020

Advances in Mathematical Physics

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Based on the weighted complex network model, this paper establishes a multiweight complex network model, which possesses several different weights on the one edge. According to the method of network split, the complex network with multiweights is split into several different complex networks with single weight. Some new static characteristics, such as node weight, node degree, node weight strength, node weight distribution, edge weight distribution, and diversity of weight distribution are defined. Then, by using Lyapunov stability theory, the adaptive feedback synchronization controller is designed, and the complete synchronization of the new complex network model is investigated. Two numerical examples of a triweight network model with the same and diverse structure are given to demonstrate the effectiveness of the control strategies. The synchronization design can achieve good results in the same and diverse structure network models with multiweights, which enrich complex network and control theory, so has certain theoretical and practical significance.

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Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

Liu

Song

et al. 2022

Asian Journal of Control

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This paper investigates the non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults. First, a novel fault model consisting of linear and nonlinear terms is established for the systems. By constructing a stochastic co‐positive Lyapunov function, the non‐fragile reliable controller is designed for the systems with additive gain perturbations using matrix decomposition technique. Then, the proposed design is extended for dealing with multiplicative gain perturbations and variable gain perturbations. Under the designed controllers, the resulting closed‐loop systems are positive and stochastically stable. All presented conditions are solvable in terms of linear programming. Finally, two illustrative examples are provided to verify the effectiveness of the theoretical results.

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Synchronization of discrete-time Markovian jump complex dynamical networks with random delays via non-fragile control

Cited by 21 publications

References 35 publications

A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

A New Complex Network Model with Multiweights and Its Synchronization Control

Non‐fragile reliable control of nonlinear positive semi‐Markovian jump systems with nonlinear actuator faults

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