The relatively new concept of wave-based control is extended to general, finite-dimensional, linear, time-invariant systems, with or without damping. The new models offer an explanation for how systems of springs and masses although lumped, and therefore, technically having no delay appear to have delay nonetheless. The principal contribution is a fairly systematic, multi-input multi-output, multi-objective control design methodology. The method yields controllers which in general deliver good closed-loop tracking, good disturbance rejection, and good stability robustness in the face of parameter uncertainty. In particular, but not exclusively, the method is applicable to the control of flexible structures as demonstrated by several examples including mitigation of sloshing of liquid-fuel in a simplified model of an upper-stage Vega rocket.

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