A FIXED POINT THEOREM APPROACH TO GENERALIZED HALANAY INEQUALITIES
DOI:
https://doi.org/10.18173/2354-1059.2025-0034Keywords:
Halanay inequalities, exponential stability, fixed point theoremAbstract
In this paper, we aim to reformulate a generalized Halanay inequality. A new approach using fixed point theorems for contraction mappings is presented. The obtained estimation can be utilized in various problems for nonlinear time-delay systems such as stability, dissipativity analysis and control design.
References
[1] Tian HJ, Fan LQ & Xiang JX, (2007). Numerical dissipativity of multistep methods for delay differential equations. Applied Mathematics and Computation, 188, 934–941.
[2] Liu B, Lu W & Chen T, (2011). Generalized Halanay inequalities and their applications to neural networks with unbounded time-varying delays. IEEE Transactions on Neural Networks, 22, 1508–1513.
[3] Hien LV, Phat VN & Trinh H, (2015). New generalized Halanay inequalities with applications to stability of nonlinear non-autonomous time-delay systems. Nonlinear Dynamics, 82, 1–13.
[4] Wen L, Yu Y & Wang W, (2008). Generalized Halanay inequalities for dissipativity of Volterra functional differential equations. Journal of Mathematical Analysis and Applications, 347, 169–178.
[5] Ruan D & Liu Y, (2019). Generalized Halanay inequalities with applications to generalized exponential stability and boundedness of time-delay systems. Mathematical Problems in Engineering, 2019, 1–7.
[6] Lu B, Jiang H, Abdurahman A & Hu C, (2016). Global generalized exponential stability for a class of nonautonomous cellular neural networks via generalized Halanay inequalities. Neurocomputing, 214, 1046–1052.
[7] Wu Q, Zhang H, Xiang L & Zhou J, (2012). A generalized Halanay inequality on impulsive delayed dynamical systems and its applications. Chaos, Solitons & Fractals, 45, 56–62.
[8] Halanay A, (1966). Differential Equations: Stability, Oscillations and Time Lags. Academic Press, London.
[9] Walter W, (1970). Differential and Integral Inequalities. Springer-Verlag, Berlin.
