Which discretization method guarantees stability preservation?

• A. Zero-Order Hold
• B. Tustin method
• C. Forward Euler
• D. Backward Euler

Answer: (B)

The Tustin method, also known as the bilinear transformation, is recognized for maintaining stability when converting continuous-time systems into discrete-time systems. This method achieves stability preservation through a mapping that transforms the s-plane into the z-plane, specifically by using a substitution that ensures that poles of the continuous system that are inside the left half of the s-plane remain inside the unit circle in the z-plane.

This characteristic makes the Tustin method particularly valuable when working with systems that require rigorous stability criteria. By preserving the stability of the original continuous-time system, the Tustin method allows engineers to design and analyze discrete systems while maintaining the desired performance — providing a robust approach in control system design.

In contrast, the other discretization methods, such as the Zero-Order Hold, Forward Euler, and Backward Euler, may not guarantee stability preservation under all conditions. For example, simple approximations like the Forward Euler method can lead to stability issues if not implemented with careful consideration of the specific characteristics of the system. The Backward Euler method has better stability compared to Forward Euler in certain contexts but does not provide the same level of reliability as the Tustin method across all scenarios. Thus, the Tustin method stands out for its ability to consistently maintain stability through