Materials on Linearization of Nonlinear Systems

When studying nonlinear systems, linearization serves as a fundamental concept that involves transforming nonlinear systems into linear approximations for simplified analysis and solution derivation. Several linearization techniques exist, with Taylor series expansion and Jacobian matrix methods being the most prevalent approaches. From an implementation perspective, Taylor linearization typically requires symbolic differentiation or numerical approximation of partial derivatives, while Jacobian-based linearization involves computing the matrix of first-order partial derivatives at the operating point. It is crucial to note that linearization must be performed around a specific point of the nonlinear system, as the approximation remains valid only within a small neighborhood of that point. The selection of this operating point significantly impacts accuracy, often requiring iterative refinement in practical applications. These materials provide valuable insights into both the theoretical foundations and practical implementation of linearization techniques, including MATLAB code examples for Jacobian computation using symbolic toolbox functions like `jacobian()`, and numerical implementation strategies for real-time systems. Understanding these concepts enables better comprehension of linearization principles and their application to real-world problems such as controller design, stability analysis, and system optimization.