الفهرس 
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Abstract
A general deadbeat state-feedback control problem in linear, multivariable, discrete-time systems is posed and solved. The controller is required to transfer the system from any arbitrary initial state to the origin of the state space in a prescribed number N of time steps (sampling intervals); N can take on any integral value between (and including) an upper limit equal to n and a lower limit equal to vc where n is the order of the system and vc is the controllability index. The solution is developed in such a way that the inherent nonuniqueness of the controller structure is wholly displayed and conveniently organized. The situation of minimum-time deadbeat control (N=vc) emerges as a mere special case.
A = properly parametrized control law is developed, where the minimum number u of free parameters are incorporated. The formula for u is simple and is expressed in terms of the number of controlinputs and the different numbers of the closed-loop eigenvectors and generalized eigenvectors. A convenient arrangement for the u free parameters withuin the structure of the control law is given. In this way, all possible solutions for the deadbeat control problem can be generated without parameter redundancy.
It is found that the desired control action is achievable by a family of classes of deadbeat controllers. The number of classes is equal to the number of allowable jordan forms of the closed-loop system. Each class is characterized by a specific number u of free parameters. By varing the values of such parameters, an infinite number of deadbeat controllers (belonging to the same class) are produced.