Background:
In control systems, the Open Loop Transfer Function (OLTF) is the transfer function of the system without any feedback. The s-plane is a complex plane used to analyze the behavior of control systems. Stability of a control system is crucial for its proper functioning. A stable system will settle to a steady state, while an unstable system will exhibit oscillatory or divergent behavior.

Explanation:
When the OLTF contains one zero in the right half of the s-plane, it indicates that the system has at least one pole in the right half of the s-plane. This can lead to instability in the closed-loop system, especially for higher gain values. Let's understand this in detail:

1. Open Loop Transfer Function (OLTF):
The OLTF is the transfer function of the system without any feedback. It represents the relationship between the input and the output of the system. The OLTF is given by:

OLTF(s) = G(s)H(s)

Where G(s) is the transfer function of the plant or process and H(s) is the transfer function of the controller.

2. Zero in the Right Half of the s-plane:
When the OLTF contains a zero in the right half of the s-plane, it means that the numerator of the OLTF has a factor (s - z), where z is a complex number with a positive real part. This indicates that the system has at least one pole in the right half of the s-plane.

3. Stability of the Closed Loop System:
The stability of the closed-loop system depends on the location of the poles of the OLTF. If all the poles of the OLTF are in the left half of the s-plane (i.e., they have negative real parts), the closed-loop system will be stable.

4. Unstable Closed Loop System:
When the OLTF has at least one pole in the right half of the s-plane, it can lead to instability in the closed-loop system. This is because the presence of a pole in the right half of the s-plane introduces exponential growth or oscillations in the system response.

5. Influence of Gain:
For higher gain values, the closed-loop system becomes more sensitive to the presence of poles in the right half of the s-plane. The gain amplifies the effect of the poles, leading to increased instability.

Conclusion:
In summary, when the OLTF contains one zero in the right half of the s-plane, the closed-loop system is unstable, especially for higher gain values. This is because the presence of a pole in the right half of the s-plane can introduce instability and oscillations in the system response. It is important to design the control system carefully to ensure stability and proper functioning.