In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first-order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology.
This topic includes the following resources and journeys:
With a general understanding of linearization, you might run into a few snags when trying to linearize realistic nonlinear models. These snags can be avoided if you have a more practical...See More
Why go through the trouble of linearizing a model? To paraphrase Richard Feynman, it’s because we know how to solve linear systems. With a linear model we can more easily design a controller...See More
This lecture describes how to obtain linear system of equations for a nonlinear system by linearizing about a fixed point. This is worked out for the simple pendulum "by-hand" and in...See More
In this video we show how to use the Linear Analysis Tool to trim a non-linear Simulink model. This is also known as finding an operating point or an equili...See More
In this video we show how to linearize a non-linear Simulink model using numerical techniques. This approach is extremely powerful as it allows automatic ge...See More