Finite-time control for a class of discrete-time systems with time delay

Finite-time stability can be used in all applications where large values of the state are not acceptable. In this paper, we extend the concept of finite-time boundedness (FTB) for a class of linear discrete-time systems with time delay and time varying exogenous disturbances. Then, we present a new approach for finite-time control problems for these discrete-time systems. The main results provided are sufficient conditions for robust finite-time stabilization via state feedback. The conditions can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). Finally, an illustrative example is given to demonstrate the validity of the proposed methodology.