Singularly perturbed unified systems with low sensitivity to model reduction

A method of designing a state feedback gain achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the delta operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system. The present paper extends the previous study to the discrete system and the delta operating system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.