The application of genetic algorithm on control of discrete multiple time- delay singularly perturbation systems

In this paper, we propose a new optimal control design algorithm with compact form for discrete multiple time-delay singularly perturbed systems by using the metagenetic algorithm. The corresponding compact slow and fast subsystems of the original discrete singularly perturbed system are first derived. The compact state feedback controllers for the slow and the fast subsystems are then separately designed by a metagenetic algorithm and then a composite state feedback controller for the original system is after synthesized. Finally, a ε -dependent stability condition in frequency domain for the original system under the compact composite state feedback controller is then considered. Stability of original system is confirmed by establishing that of its corresponding slow and fast subsystems if any one criteria of the condition is satisfied.