The current article gives a new approach that is efficient for the design of a low-order H∞ controller over a finite time interval. The system under consideration is a linear discrete time system affected by norm bounded disturbances. The proposed method has the advantage that takes into account both robustness aspects and desired closed-loop characteristics, reducing the number of variables in Linear Matrix Inequalities (LMIs). Thus, reduced order H∞ controller parameters are given to guarantee a finite time H∞ bound (FTB-H∞) for a closed-loop system. The method of the finite time stability, that is proven in this paper by the Lyapunov theory, can be applied to a wide range of process models. Numerical examples demonstrating the effectiveness of the results developed are presented at the end of this paper.
