# Linearization

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.

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## Trimming and Linearization, Part 2: The Practical Side of Linearization

11 min
Beginner
Video
Theory

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...

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## Trimming and Linearization, Part 1: What is Linearization?

14 min
Beginner
Video
Theory

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...

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## Linearizing Around a Fixed Point [Control Bootcamp]

30 min
Beginner
Video
Theory

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...

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## Control Design Onramp with Simulink

60 min
Beginner
Software
Demonstration

Learn the basics of feedback control design in Simulink®. Adjust the gains of a PID controller to change the dynamics of a physical system and get the closed-loop system behavior that you...

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## Numerically Linearizing a Dynamic System

104 min
Beginner
Video
Theory

In this video we show how to linearize a dynamic system using numerical techniques. In other words, the linearization process does not require an analytical...

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## Trimming a Simulink Model Using the Linear Analysis Tool

68 min
Beginner
Video
Application

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...

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## Linearizing a Simulink Model Using the Linear Analysis Tool and ‘linmod’

55 min
Beginner
Video
Application

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...

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