Control Theory: Boundaries of Attainability. Novel Interpretation of Robustness

In pole placement method, what are the limitations of assigning new pole positions? How can I see that if I, for example, assign a pole from +2 to -100000, there is no practical application? Originally asked on Quora.

Answer by Egor Polilov, Lead Programmer at NTR Lab, on Quora:

Q1Fig. 1. The key idea and main result

SO, NOVEL INTERPRETATION OF ROBUSTNESS IN CONTROL THEORY AND
THE BOUNDARIES OF ATTAINABILITY OF AUTOMATIC CONTROL THEORY: Ri(x)/Ri(0) <1

Q2 (2)

Q3 (2)

Q4 (2)

Q5 (2)

Q6 (2)

Q7Fig. 3. Ideal tracking problem

Excerpted from the original article [in Russian] by E.V. Polilov,  Assessment Of Borders For Large Deviations Of Phase Variables In Linear Systems  / DonSTU scientific works collection Р2016, Alchevsk, Ukraine.

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More answers from Egor:

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Control theory in control systems engineering deals with the control of continuously operating dynamical systems in engineered processes and machines. The objective is to develop a control model for controlling such systems using a control action in an optimum manner without delay or overshoot and ensuring control stability. (Wikipedia)

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