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 linearize a non-linear Simulink model using numerical techniques. This approach is extremely powerful as it allows automatic ge...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