scholarly journals Estimates for solutions to one class of nonlinear nonautonomous systems with time-varying concentrated and distributed delays

2021 ◽  
Vol 18 (2) ◽  
pp. 1689-1697
Author(s):  
I. I. Matveeva
Keyword(s):  
Distributed Delays ◽  
Time Varying ◽  
Nonautonomous Systems

scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

scholarly journals Dissipative stabilization of linear systems with time-varying general distributed delays

Automatica ◽  
2020 ◽  
Vol 122 ◽  
pp. 109227
Author(s):  
Qian Feng ◽  
Sing Kiong Nguang ◽  
Wilfrid Perruquetti
Keyword(s):  
Linear Systems ◽  
Distributed Delays ◽  
Time Varying

Extra-insensitive shaper with distributed delays: Design and vibration suppress analysis

2020 ◽  
Vol 26 (15-16) ◽  
pp. 1185-1196
Author(s):  
Yuqi Huang ◽  
Hongguang Li ◽  
Jiwen Zhou ◽  
Lili Meng
Keyword(s):  
Radial Direction ◽  
Distributed Delays ◽  
Step Response ◽  
Asymmetric Distribution ◽  
Double Pendulum ◽  
Time Varying ◽  
Distribution Method ◽  
Modeling Errors ◽  
Multi Mode ◽  
Tolerable Level

Distributed delays have proved beneficial in eliminating vibrations in higher frequency ranges compared to the modeled frequency, but not in improving the robustness against the modeled frequency to modeling errors. In this paper, the extra-insensitive shaper with distributed delays is proposed to improve robustness and efficiency for systems with a large variation of modal frequencies. The extra-insensitive shaper with distributed delays is derived by distributing two zeros in the radial direction of the designed zero of the distributed zero-vibration shaper. Two methods of distributing zeros are provided to parameterize the extra-insensitive shaper with distributed delays. Asymmetric extra-insensitive shaper with distributed delays and symmetric extra-insensitive shaper with distributed delays are two types of the extra-insensitive shaper with distributed delays parameterized by the asymmetric distribution method and the symmetric distribution method. Properties of the Asymmetric extra-insensitive shaper with distributed delays and the symmetric extra-insensitive shaper with distributed delays in spectral, sensitivity and step response are analyzed and compared with those of the classical extra-insensitive shaper and distributed zero-vibration-derivative shaper. The results present larger robustness in variations of modeled and higher frequencies, suppressing the vibration of the modeled mode and unmodeled higher multiple modes to a tolerable level. The implement in the time-varying double-pendulum crane verifies the effectivity for vibration suppress of multi-mode systems.

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