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A typical linear control strategy in discrete-time systems, deadbeat control produces transients that vanish in finite time. On the other hand, the linear-quadratic control stabilizes the system and minimizes the l2 norm of its transient response. Quite surprisingly, it is shown that deadbeat systems are l2 optimal, at least for reachable systems.
Motivated by the dead-beat and shortest-correlation control strategies, the paper introduces the notion of finite-input finite-output (FIFO) stability for linear discrete-time control systems. A simple parametrization of all controllers that FIFO-stabilize a given plant is obtained. The best controller is then chosen for various applications, including H 2 optimization, disturbance rejection...
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