Robust and Resilient Finite-Time Control of a Class of Discrete-Time Nonlinear Systems

Abstract In this paper, we address the finite-time state-feedback stabilization of a class of discrete-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. Sufficient 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 is obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere 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. We conclude the paper with a numerical example showcasing the applicability of the main result.

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