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A necessary algebraic condition for controllability and observability of linear time-varying systems

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2 Author(s)
Leiva, Hngo ; Dept. of Math., Univ. de Los Andes, Merida, Venezuela ; Siegmund, S.

In this note, we give an algebraic condition which is necessary for the system x'(t)=A(t)x(t)+B(t)u(t), y(t)=C(t)x(t), either to be totally controllable or to be totally observable, where x∈Rd, u∈Rp, y∈Rq, and the matrix functions A, B and C are (d-2), (d-1) and (d-1) times continuously differentiable, respectively. All conditions presented here are in terms of known quantities and therefore easily verified. Our conditions can be used to rule out large classes of time-varying systems which cannot be controlled and/or observed no matter what the nonzero time-varying coefficients are. This work is motivated by the deep result of Silverman and Meadows.

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Automatic Control, IEEE Transactions on  (Volume:48 ,  Issue: 12 )