- #1
Faraz Murtaza
- 32
- 0
a system is said to be stable if its impulse response approaches zero for sufficiently large time. why?
please give me an satisfying answer..
please give me an satisfying answer..
Last edited by a moderator:
mistermotown said:Let me know if that helps, or if I didn't explain it well enough.
Or if you need to know about stability in Z-transforms.
Stability theory is a branch of mathematics and engineering that deals with the study of how systems respond to perturbations or changes in their initial conditions. It aims to understand and predict the behavior of complex systems in the face of disturbances.
Impulse response is a mathematical concept used in stability theory to describe how a system responds to an impulse or sudden change in its input. It is a function that represents the output of a system when an impulse is applied to its input.
Stability refers to a system's ability to maintain its equilibrium or initial state in the face of perturbations, while instability refers to a system's tendency to deviate from its equilibrium or initial state due to perturbations. In other words, a stable system will return to its initial state after being disturbed, while an unstable system will continue to move away from its initial state.
Stability is important in engineering and science because it allows us to predict and control the behavior of systems. It is essential for ensuring the safe and efficient operation of various systems, such as airplanes, bridges, and chemical reactions. Additionally, stability is a fundamental concept in understanding the dynamics of natural phenomena, such as weather patterns and ecosystems.
There are three types of stability: stable, unstable, and neutral. A stable system returns to its initial state after being disturbed, an unstable system moves away from its initial state after being disturbed, and a neutral system remains in its new state after being disturbed. These types of stability can be further classified into local or global stability, depending on the range of initial conditions considered.