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When stabilizing linear discrete-time finite dimensional systems in control and estimation either optimally or suboptimally, technical difficulties arise in the conventional stability theories for coping with state transition matrices which are permitted to be singular or with eigenvalues arbitrarily small. In overcoming these difficulties, earlier results for feedback stabilization of linear systems and for Kalman filters and regulators are generalized in this paper, with proofs being in fact more direct than those explored earlier.
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Moore et al. (1980) studied this question.
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