Application of genetic algorithm on observer-based D-stability control for discrete multiple time-delay singularly perturbation systems

This study proposes a Genetic Algorithm (GA) application for the observerbased controller design for discrete multiple time-delay, singularly perturbed systems. The corresponding slow and fast subsystems of the original system are first determined. The GA then derives the observer-based controllers for the D-stability of the slow and the fast subsystems, and a composite observer-based controller for the original system synthesized from the designed subsystems controllers. This study proposes a stability condition dependent upon the singular perturbation parameter ε, to guarantee the stability of the original system under the composite observer-based controller. This study finds the stability criteria of the original uncontrolled system by establishing the stability criteria for its corresponding slow and fast subsystems. If any of the criteria conditions is satisfied, this study uses the condition to find the upper bound ε∗ of ε and can guarantee the stability of the original system by examining the stability of corresponding subsystems, if ε ∈ [0, ε∗). Finally, an illustrative example demonstrates the efficiency of the proposed controller.