Difference Inequalities and Application to Discrete-Time Control Systems
In this paper, 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.
Zhengyi Jiang, Xianghua Liu and Jingtao Han
Z. Y. Hou and W. S. Wang, "Difference Inequalities and Application to Discrete-Time Control Systems", Advanced Materials Research, Vols. 889-890, pp. 978-981, 2014