Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems

Finite-time state-feedback stabilization is addressed for a class of discrete-time nonlinear systems with conic-type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. First, conditions for the existence of a robust and resilient linear state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, a solution for the controller gain and the maximum allowable bound on the gain perturbation is obtained. The developed controller is robust for all unknown nonlinearities lying in a known hypersphere with an uncertain center and all admissible disturbances. Moreover, it is resilient against any bounded perturbations that may alter the controller’s gain by at most a prescribed amount. The paper is concluded with a numerical example showcasing the applicability of the main result.