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Discrete-Time Models of Continuous-Time SystemsContinuous-Time Models of Discrete-Time Systems

3.6 Discrete-Time Models of Systems with Delay

ToDiscreteTime can also find the discrete-time approximation of analog state-space systems of the form

which corresponds to systems with time delay . The systems can be represented as conventional StateSpace objects with a Delay option added. The conversion implements the modified -transform algorithm described in Franklin et al. (1990), Section 2.4.4.

Currently, ToDiscreteTime is the only function that takes the Delay option into consideration and, even more restrictively, it handles the only case of numerical values of the ratio , where is the sampling period. Negative delay is equivalent to prediction of the system's behavior and can be used as long as the delay is not longer than the sampling period.

Option in StateSpace to introduce a delay in control.

Here is a simple state-space system with delay of Lambda.

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This is its discrete-time approximation when the delay equals the sampling period.

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If the delay increases, then so does the dimension of the state space.

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This is an example of the transformation of a system with a negative delay.

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Discrete-Time Models of Continuous-Time SystemsContinuous-Time Models of Discrete-Time Systems