Abstract
The simulation of step, impulse and ramp responses of linear continuous-time time-invariant single-input single-output systems with a pure time delay in the feedback loop is tackled. Contrary to systems without time delay where a conversion from Laplace transform to z transform with a zero-order hold allows for an exact response, delay in the feedback loop requires either an unbounded number of states or approximations. This paper proposes an approximation which fulfills a set of criteria, including exactness of the response over a specified multiple of the delay and the conservation of the stability or lack of stability. The approach is illustrated with examples.
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