1. To construct and study new augmented Lyapunov-Krasovskii-like functional, which is mainly based on the information of the lower and upper delay bounds. The time delay is an interval time-varying function belonging to a given interval, which allows the time delay to be a fast time-varying function, and the lower bound is not restricted to being zero.
2. To find new delay-dependent sufficient conditions for the finite-time stability of linear discrete-time singular systems with interval time-varying delays and the stabilizing controllers to be designed must satisfy the finite-time stabilization of linear discrete-time singular systems with interval time-varying delays constraints on the closed-loop poles are established in terms of linear matrix inequalities (LMIs).
3. To be developed method using new inequalities for lower bounding cross terms eliminate the need for over bounding and provide larger values of the admissible delay bound..
4. To be applied to the finite-time stability of hybrid linear discrete-time singular systems, the finite-time stability of large-scale interconnected linear discrete-time singular systems, the finite-time stability of convex polytopic uncertainties linear discrete-time singular systems and the finite-time mean square stability of stochastic linear discrete-time singular systems with interval time-varying delays and the stabilizing controllers to be designed must satisfy the finite-time stabilization of hybrid linear discrete-time singular systems, the finite-time optimal guaranteed cost control of linear discrete-time singular systems, the finite-time stabilization of large-scale interconnected linear discrete-time singular systems, the finite-time stabilization of convex polytopic uncertainties linear discrete-time singular systems and the finite-time mean square stabilization of stochastic linear discrete-time singular systems with interval time-varying delays constraints on the closed-loop poles are established in terms of linear matrix inequalities (LMIs).
5. To find numerical examples are given to illustrate the effectiveness of the new theory.
6. To create research network both inside and outside of the country for making cooperation in doing research in this area.
