Lectures related to Approximate Linearization

Modeling Dynamic Systems: Definitions and Examples

Covers the modeling of dynamic systems, including definitions, examples, and linearization processes for easier analysis.

Applications of Laplace Transform: State Space Modeling

Explores the application of Laplace transform in state space modeling of linear systems and the control of dynamic systems.

Exact Linearization: Earth Dynamics and Stabilization

Explores exact linearization techniques for transforming non-linear systems into linear ones, emphasizing system stability.

Networked Control Systems: Fundamentals and Stability Analysis

Covers the fundamentals and stability analysis of Networked Control Systems, including software installation, dynamical systems, equilibrium states, and stability testing.

Convolution and Laplace Transform

Explores control of dynamic systems, impulse response, Laplace transform, and Fourier transform for solving differential equations.

Linear Systems in 2D: Stability

Explores stability in linear 2D systems, covering fixed points, vector fields, and phase portraits.

Introduction to Nonlinear Systems Control

Covers the analysis and control of nonlinear systems, including methods like phase plan and passivity.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

SISO Polynomial Controllers: Sylvester Matrix, Internal Model Principle

Covers the design of SISO polynomial controllers using concepts such as the Sylvester matrix and model matching.

Dynamic Systems: Formalism and Bases

Covers the formalism and bases of dynamic systems, including differential equations and non-linear systems.

Multivariable Control: System Theory and Linear Systems

Introduces multivariable control, covering system theory, linear systems, and time discretization.

Phase Plan: Linear Order Systems

Discusses phase plans for linear order systems and characterizing trajectories through distinguishing eigenvalues and equilibrium points.

Stability Analysis: Linear Systems

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Control Systems Review: LTI Systems

Covers linear, causal, and time-invariant systems, with practical examples and MATLAB simulations.

Multivariable Control: System Theory and Linear Systems

Introduces the basics of multivariable control, focusing on system theory and linear systems.

1st Harmonic: Stability and Adaptation

Covers stability, adaptation, Nyquist criterion, and predicting limit cycle existence.

Lyapunov Stability Theory: Energy Functions and Stability Analysis

Covers Lyapunov stability theory, energy functions, positive-definite matrices, and system stability analysis through examples and theorems.

Dynamic Systems: Course Review

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

State-space Modeling Log in to Mediaspace to watch this video

Introduces the state-space approach to modeling dynamical systems and its utility for high-speed solution of differential equations and computer algorithms.

Approximate linearization Log in to Mediaspace to watch this video

Explains the procedure of linearizing a non-linear system around equilibrium points.