Review of stability and stabilization for impulsive delayed systems

Xiao, Yang; Li, Xiaodi; Xi, Qiang; Duan, Peiyong

doi:10.3934/mbe.2018069

Cited by 164 publications

(69 citation statements)

References 118 publications

(179 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent times, differential equation and fractional differential equation models have found their applications in a variety of fields including biology [1][2][3][4][5][6], physics [7][8][9][10], engineering [11][12][13][14], mathematics [15][16][17][18], information technology, and so on [19][20][21][22][23][24][25][26][27]. They are also one of the most rudimentary tools for neural networks.…”

Section: Introduction and Modelingmentioning

confidence: 99%

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

et al. 2020

View full text Add to dashboard Cite

In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.

show abstract

Section: Introduction and Modelingmentioning

confidence: 99%

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

et al. 2020

View full text Add to dashboard Cite

show abstract

“…As is well known, the time delays can influence the dynamic of systems seriously and may cause some unstable performances such as divergence, oscillation or chaotic. Over the past few years, a great number of research papers have been published to focus on the stability and stabilization of dynamical systems with time delays (see [1][2][3][4][5][6] and the references cited therein). At the same time, it should be mentioned that under some exogenous disturbances, the system states may evolve in a bounded domain rather than converge to an equilibrium point, which indicates that the conventional stability cannot be realized.…”

Section: Introductionmentioning

confidence: 99%

Event-based robust stabilization for delayed systems with parameter uncertainties and exogenous disturbances

2020

Adv Differ Equ

View full text Add to dashboard Cite

In this paper, the robust stabilization problem is studied for a class of delayed systems with parameter uncertainties and unknown-but-bounded exogenous disturbances. The robust input-to-state practical stability (RISpS) is introduced to characterize the dynamics of the controlled system. An event-triggered strategy is employed to effectively decrease the transmission consumption of the robust controller. The Zeno behavior is also excluded by combining the information of delayed states with parameter uncertainties. The gain matrix and the event-triggered parameters are co-designed by resorting to the feasibility of several matrix inequalities. An example and its simulations are given to illustrate the proposed approach.

show abstract

“…Moreover, the performance of the closed‐loop system may be degraded if time delay is not taken into consideration, and even destabilization of the control system maybe occur. Therefore, impulsive delay systems are popular with many authors in the last years because of their plenty of real applications . Furthermore, Razumikhin technique and Lyapunov‐Krasovskii functional approach have been applied to obtain sufficient conditions of ISS and iISS for time‐delay systems.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, impulsive delay systems are popular with many authors in the last years because of their plenty of real applications. 30,[34][35][36][37][38] Furthermore, Razumikhin technique 30,31 and Lyapunov-Krasovskii functional approach 39 have been applied to obtain sufficient conditions of ISS and iISS for time-delay systems. To the best of our knowledge, impulsive interval and time delay are conservatively dealt with by previous methods.…”

Section: Introductionmentioning

confidence: 99%

Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

Jiang

et al. 2019

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

Summary In this paper, input/output‐to‐state stability (IOSS) and integral IOSS (iIOSS) are investigated for nonlinear impulsive systems with delay. Based on a new impulsive inequality, we propose some sufficient criteria for IOSS and iIOSS of impulsive delay systems. It is shown that the obtained results for IOSS and iIOSS are regardless of the length of the impulsive interval and the size of time delay if the impulsive gain satisfies a given condition. In addition, based on the average impulsive interval method, some more useful sufficient conditions are derived for IOSS and iIOSS of impulsive delay systems with persistent large‐scale destabilizing impulses. Furthermore, a relationship is established among the average impulsive interval, impulses, time delay, and the decay of the system without impulses such that the impulsive delay system is input/output‐to‐state stable and integral input/output‐to‐state stable, respectively. Two examples are given to show the validity of the obtained results.

show abstract

Review of stability and stabilization for impulsive delayed systems

Cited by 164 publications

References 118 publications

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks

Event-based robust stabilization for delayed systems with parameter uncertainties and exogenous disturbances

Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

Contact Info

Product

Resources

About