On Zeros of Discrete-Time Models for Collocated Mass-Damper-Spring Systems

When a continuous-time system is discretized using the zero-order hold, there is no simple relation which shows how the zeros of the continuous-time system are transformed by sampling. In this paper, for a discrete-time model of a collocated mass-damper-spring system, the asymptotic behavior of the zeros is analyzed with respect to the sampling period and the linear approximate expressions are given. In addition, the linear approximate expressions lead to a sufficient condition for all the zeros of the discrete-time model to lie inside the unit circle for sufficiently small sampling periods. The sufficient condition is satisfied when a damping matrix is positive definite. Moreover, an example is shown to illustrate the validity of the linear approximations. Finally, a comment for a noncollocated system is presented.

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