AUTHORS: Magdi S. Mahmoud

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ABSTRACT: The paper provides complete results of the feedback control design problem for a wide class of discretetime systems possessing fast and slow modes. The mode-separation is expressed in terms of an inequality relating norms of system sub-matrices. The slow and fast subsystems are considered to be completely controllable and observable. A systematic two-stage procedure is developed which enables designing separate gain matrices for the fast and slow subsystems based on H∞ and H2 optimization criteria and using linear matrix inequalities. It is established that the composite control yields first-order approximations to the behavior of the discrete system. The theoretical analysis is extended to designing of Kalman filters and linear quadratic Gaussian controllers. It is shown that the design procedure eventually reduces to solving pure-slow and pure-fast reduced-order Kalman filters followed by pure-slow and pure-fast reduced-order discrete-time algebraic Riccati equations. Typical applications are considered to illustrate the design procedure.

KEYWORDS: Time-scale modeling; Composite control; Linear quadratic Gaussian; Kalman filter; Slow subsystem; Fast subsystem

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