Determining Stability of a continuous time system using Laplace Transform

1. How do you find the stability of a Laplace transform?
2. What are the real life applications of Laplace transform?
3. How Laplace transform is used in control system?

How do you find the stability of a Laplace transform?

below can all be derived and understood by expansion of H(s) ⁢ in terms of partial fractions, and then doing a inverse Laplace transform fraction by fraction. zi denotes the zeros and pi denotes the poles of the linear time invariant system (LTI).

What are the real life applications of Laplace transform?

Laplace transform is an integral transform method which is particularly useful in solving linear ordinary dif- ferential equations. It finds very wide applications in var- ious areas of physics, electrical engineering, control engi- neering, optics, mathematics and signal processing.

How Laplace transform is used in control system?

The Laplace transform plays a important role in control theory. It appears in the description of linear time invariant systems, where it changes convolution operators into multiplication operators and allows to define the transfer function of a system.