Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

Li, Lianzhong; Meng, Fanwei; Ju, Peijun

doi:10.1016/j.jmaa.2010.12.002

Cited by 46 publications

(28 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[1][2][3][4][5][6][7][8][9] However, these methods depend on the known upper bounds of unknown time-delays in inputs or states. Hence, study for nonlinear time-delayed systems is significative both in theory and in practice.…”

Section: Introductionmentioning

confidence: 99%

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

Zhou

Liu

Cao

et al. 2019

Adaptive Control & Signal

View full text Add to dashboard Cite

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional-order time-varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi-Sugeno fuzzy method. An adaptive controller together with fractional-order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed-loop system and the Mittag-Leffler stability of tracking error can be guaranteed. T-S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.

show abstract

Section: Introductionmentioning

confidence: 99%

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

Zhou

Liu

Cao

et al. 2019

Adaptive Control & Signal

View full text Add to dashboard Cite

show abstract

“…Liang et al extend the study of Lazarević et al and Luo et al to study a second order–delayed system based on the notation of delayed matrix cosine/sine of a polynomial of degree. For more recent contributions, we refer the reader to several previous studies . However, to our best knowledge, finite‐time stability of oscillating systems with 2 delays have not been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

“…For more recent contributions, we refer the reader to several previous studies. [25][26][27][28][29][30][31][32][33][34][35] However, to our best knowledge, finite-time stability of oscillating systems with 2 delays have not been studied extensively.…”

Section: Introductionmentioning

confidence: 99%

Finite‐time stability of a class of oscillating systems with two delays

Cao

Wang

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we study finite‐time stability of an oscillating system with 2 delays. To derive a bounded of state vector, we use a representation of explicit solution involving 2‐delayed matrix polynomial of 2 indices after deriving some fundamental estimates for such delayed matrix polynomial of 2 indices. A sufficient condition is given. Finally, an example is given to demonstrate the application of the main result.

show abstract

“…Time-varying delays are used to indicate the promoted speed of signals is finite and uncertain in systems [21][22][23][24][25][26][27][28]. Noting that while signal propagation is sometimes instantaneous and can be modeled with discrete delays, it may also be distributed during a certain time period so that distributed delays are incorporated into the model [29].…”

Section: Introductionmentioning

confidence: 99%

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Yogambigai

Ali

Zhu

et al. 2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The problem of exponential Lagrange stability analysis of Markovian jump neural networks with leakage delay and mixed timevarying delays is studied in this paper. By utilizing the Lyapunov functional method, employing free-weighting matrix approach and inequality techniques in matrix form, we establish several novel stability criteria such that, for all admissible parameter uncertainties, the suggested neural network is exponentially stable in Lagrange sense. The derived criteria are expressed in terms of linear matrix inequalities (LMIs). A numerical example is provided to manifest the validity of the proposed results.

show abstract

Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

Cited by 46 publications

References 10 publications

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

Finite‐time stability of a class of oscillating systems with two delays

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

Contact Info

Product

Resources

About