In this paper, we show the relations between the polynomial and the strictly proper rational portions of the polynomial matrix fraction P(s)Q~ '(s)R(s), where P(s)Q~i(s) and Q ~1 (s)R(s) are both strictly proper. It is also shown that if Q ~l (s)R{s) (P(s)Q " ' (s)) is given, P(s)(R(s)) is uniquely defined by the strictly proper portion of the system.
In this paper, we show the relation between state space approach and transfer function approach for functional observer and state feedback design. Two approaches can be transformed into each other, based on this result. More importantly, we find that th= scate space approach introduces some severe, unnecessary restrictions in solving the problem. The restrictions are, however, reduced to be a trivial condition in transfer function approach. It is believed that the result presented in this paper will be useful in developing both approaches, and motivate some new results for solving the problem.
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