Which condition would signify that a transfer function has an unstable system?

A transfer function characterizes the relationship between input and output in a system, particularly in control systems and signal processing. Stability in a system is fundamentally linked to the locations of the poles of its transfer function.

If at least one pole is located in the right half of the complex plane, which corresponds to having a positive real part, this indicates that the system is unstable. Such poles can lead to solutions that grow unbounded over time when the system is subject to an input, as they correspond to exponentially increasing functions in the time domain. This is the hallmark of an unstable system.

In contrast, if all poles were negative, the system would be stable, as all poles would contribute to a decaying response. Conditions regarding zeroes being negative or values for ( s ) being real don’t directly inform us about the system’s stability. The presence of poles is the key factor to ascertain whether a system is stable or unstable. Understanding the significance of pole locations helps in designing and analyzing control systems effectively.