Linearizing Nonlinear Systems – State Space Approach

Real world physical and engineering systems are, typically, nonlinear. Yet, the mathematical models that we are best able to analyze and study are linear. The videos below discuss the process of coming up with linear approximations to nonlinear systems, and using the linear analysis to infer behavior of the nonlinear systems.

Practical Review of Taylor Series

An important idea behind the process of “linearization” is that of the Taylor Series. Here, I provide a practical review for those of you who cannot readily recall the basics. I use Matlab’s MuPad symbolic analysis tool to generate the terms in the series and to plot the results.

Linearization, Part A

We are going to split the process of linearization into two parts. In the first, we explore the nonlinear character of the example system a bit and then numerically compute the location of a nontrivial equilibrium.

Linearization, Part B

Now we calculate the linearization itself and check to see how well solutions to the linearized system approximate solutions to the full nonlinear system.

To get an electronic copy of the MuPad file I created in making this video, click here.

Theory

More coming…. just not soon.