Theoretical performance limits of controlled systems which interact with dynamic environments are analyzed from consideration of simple, single-axis mass-spring-damper systems. A measure of interaction control performance is defined which is independent of environment dynamics. It is shown that unmodelled dynamics between actuators and sensors places severe constraints on interaction control performance. An ultimate performance limit to guaranteed-stable interaction control is derived. A general algorithm is proposed for the design of guaranteed-stable interaction controllers which applies to arbitrary linear, time-invariant systems, and which approaches the optimal admittance while providing good disturbance rejection. The approach is illustrated in simulations.

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