Two new nonlinear difference inequalities are considered, where the inequalities consist of multiple iterated sums, and composite function of nonlinear function and unknown function may be involved in each layer. Under several practical assumptions, the inequalities are solved through rigorous analysis, and explicit bounds for the unknown functions are given clearly. Further, the derived results are applied to the stability problem of a class of linear control systems with nonlinear perturbations.
Hong Zhou. Deqing Huang. Wu-Sheng Wang. Jian-Xin Xu. "Some New Difference Inequalities and an Application to Discrete-Time Control Systems." J. Appl. Math. 2012 1 - 14, 2012. https://doi.org/10.1155/2012/214609