Invariant distributions are defined for discrete-time nonlinear control systems, and necessary and sufficient conditions are given for their controlled invariance. This extends to discrete-time systems the basic tool which has been so important in solving the various synthesis problems for continuous-time systems. To indicate their utility in the discrete-time setting, they are used to locally solve the disturbance decoupling problem.
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Jessy W. Grizzle (1985) studied this question.
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