Finite-time bounded state-dependent control of a class of discrete-time nonlinear systems

A finite-time state-feedback controller with a state-dependent gain is derived for a class of discrete-time nonlinear systems with state-dependent system matrices and additive disturbances. The controller designed yields a closed-loop system, where the state of the system does not exceed a prescribed threshold for given bounds on the initial states of the system and the additive disturbance. The controller is robust for all additive bounded perturbations to the system matrices. Moreover, it is resilient against additive perturbations in the gain which may affect its desired performance. A set of state-dependent conditions which guarantee the existence of such a controller is derived. A solution for the controller gain is obtained at each time instant through solving a set of state-dependent linear matrix inequalities. The paper is concluded with a numerical example illustrating the applicability of the proposed design approach.