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Before proceeding further, it is necessary to establish whether the resulting continuous model matches the given discrete conditions.
So, applying transformation rules, the system function is obtained
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We now check with a few test cases whether it accurately describes the dynamics of a given process.
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Enough examples.
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Conclusion: the model correctly describes a given discrete process.
You can now move on to the second part of the task - stream splitting.
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It's not easier that way:
Or are you deliberately separating these members?
Forgive me if this is off-topic, but are you trying to figure out how to eat the fish and get away with it?
Forgive me if this is off-topic, but are you trying to figure out how to eat the fish and stay dry?
how to periodically eat the fish so that it stays alive and still grows at the maximum rate.
Pinch off once a year 'for life' and let it keep growing. Is there a perfect solution to this problem? The "for life" variable is the defining one. I must be wrong, though, since I've got 11 spellings of formulas and "nerdy" words.
how to periodically eat fish so that they stay alive and still grow at the maximum rate.
then "how to eat fish as much as possible, but keep it alive until retirement" // the fish bourgeois exploiter's conundrum
The fish is an inaccurate metaphor.
It's not easier that way:
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Or are you deliberately separating these dicks?
No... I, on the contrary, move away from the discrete representation specifically to the smooth function representation. In doing so, I get a coupling factor between the two representations.
Why? Because to have a description of a continuous process and then to be able to get a smooth derivative of that process -- not that power series representation you're trying to get away from.
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A couple more clarifying questions: are you familiar with the transfer function technique? and the Laplace transform technique for solving diff equations? -- since these are necessary conditions for operating transfer functions.
In particular, the block of the circuit designated as 1/s means integration and, accordingly, the value entering it is the derivative of the output value of the block.