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This paper considers the positive real property of the impedance matching controller for double cascade-connected damped mass-spring systems, whose mass is connected to beyond the adjacent masses. The system can be regarded as a linearized model of a tensegrity beam, one of the basic structures in tensegrity systems corresponding to a cantilevered beam in continuum case. In our previous work, we considered wave analysis and control of the systems, and showed that the impedance matching controller is effective for vibration suppression of the tensegrity beam. However, in the paper, analytical property of the impedance matching controller, i.e., positive real property, was not investigated; and thus the closed loop stability is not guaranteed from the theoretical point of view. This paper addresses this issue, and shows that the impedance matching controller is actually a positive real function.

On the positive real property of the impedance matching controller for double cascade-connected damped mass-spring systems