Some new criteria for generalized contraction of differential systems with delays
Main Article Content
Abstract
In this paper, we generalize the concept contraction to generalized contraction of nonlinear differential systems with time-varying delays. Then we present some new sufficient conditions for generalized contraction of the mentioned systems. An example is given to illustrate the obtained results.
Keywords
Generalized contraction, Global contraction, Delay differential system
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
References
Aminzare, Z., & Sontag, E. D. (2015). Contraction methods for nonlinear systems: A brief introduction and some open problems. Proceedings of 53rd IEEE Conference on Decision and Control, 3835-3847.
Hale, J. K., & Lunel, S. M. V. (1993). Introduction to functional differential equations. New York: Springer.
Ky, T. Q. (2021). Exponential contraction of switching jump diffusions with a hidden Markov chain. Statistics and Probability Letters, 109191.
Lohmiller, W., & Slotine, J. J. E. (1998). On contraction analysis for nonlinear systems.
Automatica, 34, 683-696.
Ngoc, P. H. A. (2021). Contraction of stochastic differential equations. Communications in Nonlinear Science and Numerical Simulation, 95, 105613.
Ngoc, P. H. A. (2015). Novel criteria for exponential stability of nonlinear differential systems with delay. IEEE Transactions on Automatic Control , 60, 485-490.
Ngoc, P. H. A. (2012). Stability of positive differential systems with delay. IEEE Transactions on Automatic Control, 58(1), 203-209.
Ngoc, P. H. A., Trinh, H, Hieu, L. T., & Huy, N. D. (2019). On contraction of nonlinear difference systems with time-varying delays, Mathematische Nachrichten, 292(4), 859-870.
Ngoc P. H. A., & Trinh, H. (2018). On contraction of functional differential equations. SIAM Journal on Control and Optimization, 56(3), 2377-2397.
Thúy, Đ. L., Tình, C. T, Hiếu, L. T., & Vân, L. H. M. (2020). Điều kiện đủ cho tính chất epsilon-co của một lớp hệ phương trình sai phân phi tuyến với biến liên tục. Science and Technology Development Journal - Natural Sciences, 3(3), 213-224.
Hale, J. K., & Lunel, S. M. V. (1993). Introduction to functional differential equations. New York: Springer.
Ky, T. Q. (2021). Exponential contraction of switching jump diffusions with a hidden Markov chain. Statistics and Probability Letters, 109191.
Lohmiller, W., & Slotine, J. J. E. (1998). On contraction analysis for nonlinear systems.
Automatica, 34, 683-696.
Ngoc, P. H. A. (2021). Contraction of stochastic differential equations. Communications in Nonlinear Science and Numerical Simulation, 95, 105613.
Ngoc, P. H. A. (2015). Novel criteria for exponential stability of nonlinear differential systems with delay. IEEE Transactions on Automatic Control , 60, 485-490.
Ngoc, P. H. A. (2012). Stability of positive differential systems with delay. IEEE Transactions on Automatic Control, 58(1), 203-209.
Ngoc, P. H. A., Trinh, H, Hieu, L. T., & Huy, N. D. (2019). On contraction of nonlinear difference systems with time-varying delays, Mathematische Nachrichten, 292(4), 859-870.
Ngoc P. H. A., & Trinh, H. (2018). On contraction of functional differential equations. SIAM Journal on Control and Optimization, 56(3), 2377-2397.
Thúy, Đ. L., Tình, C. T, Hiếu, L. T., & Vân, L. H. M. (2020). Điều kiện đủ cho tính chất epsilon-co của một lớp hệ phương trình sai phân phi tuyến với biến liên tục. Science and Technology Development Journal - Natural Sciences, 3(3), 213-224.