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Could we stabilize our system (discrete vision of the satellite) by adding a zero? Which one is the feasible region?

Theoretically adding a single real zero between the origin and 1 could stabilize the system, but isolated zeros are not physically possible. The region satisfying our design specifications is to the left of the region of frequency equal to 0.3 (always inside the unit circle) and inside the region of damping factor bigger or equal than 0.5

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Yes, adding a single real zero between the origin and 1 will stabilize the system. The region satisfying our design specifications is to the left of the region of frequency equal to 0.3 (always inside the unit circle) and inside the region of damping factor bigger or equal than 0.5

Theoretically any zero in the left semiplane could stabilize the system, but we have to be aware not to put in on the origin or it would decrease the type (and precision ) of the system. The region satisfying our design specifications is further away than the circle of frequency equal to 0.3 and inside radiating line of damping factor equal to 0.5

Yes adding a single real zero between the origin and 1 will stabilize the system and he region satisfying our design specifications is to the left of the region of frequency equal to 0.3 (as close to minus infinite as possible) and inside the region of damping factor bigger or equal than 0.5

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