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

Finite-time state-feedback stabilization of a class of continuous-time nonlinear systems with conic type nonlinearities, bounded feedback control gain perturbations, and additive disturbances is presented. Sufficient conditions for the existence of a robust and resilient linear finite-time state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, solutions for the controller gain and the upper bound on the gain perturbations are obtained. The developed controller is robust for all unknown nonlinearities lying in a hyper-sphere and all admissible disturbances. Furthermore, it is resilient against any bounded perturbations that may modify the controller's gain by at most a prescribed amount. We conclude the paper with a numerical example illustrating the applicability of the main result.