Optimization and Control of Dynamic Systems by Henryk Górecki

Author:Henryk Górecki
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Then, the formula (8.7) takes the form

(8.13)

The integral (8.13) exists if and only if the degree of the numerator L(s) is less that the degree of the denominator M(s), that is, when the conditions of a physical realizability are satisfied.

The central idea while calculating the integral (8.13) is to break it up to such two parts that each such part can be calculated using residues in the area which does not have poles.

Therefore, let

(8.14)

Note that polynomial N(s) is at best one degree lower than the degree of M(s). Therefore, we can write

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