Lectures related to Passivity: I

Discrete-Time LTI Systems

Covers the analysis of discrete-time LTI systems, including sampling systems and system responses.

Circle Criterion: Stability and Nonlinearity

Covers the concept of passivity in linear systems and the circle criterion for absolute stability.

DC Circuits: Resistors Grouping

Explains resistor grouping in DC circuits, calculating equivalent resistance and current distribution.

Passivity, Stability and Circle Criterion

Covers passivity, absolute stability, and the circle criterion in linear systems with feedback.

Riemannian connections

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Linear Systems: Direct Methods

Covers the formulation of linear systems, direct and iterative methods for solving them, and the cost of LU factorization.

Comparing Tangent Vectors: Parallel Transport

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.

Active, Reactive, and Apparent Powers - Exercise 3

Covers the resolution of an exercise on active and reactive powers under an alternating voltage.

Parallel Transport and Geodesics

Explores parallel transport along curves and geodesics maximizing proper time between points.

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.

1st Harmonic: Stability and Adaptation

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

Stability of LTI Systems: Equilibria and Lyapunov Theory

Covers equilibria, stability analysis, and Lyapunov theory in linear systems, focusing on eigenvalues and stability properties.

Multivariable Control: System Theory and Applications

Covers system theory, classic feedback control, and applications in green building and natural gas refrigeration plants.

Linear Systems: Continuous Time

Covers linear systems in continuous time, stability analysis, and mass-spring system examples.

Connections: motivation and definition

Explores the definition of connections for smooth vector fields on manifolds.

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.

Multivariable Control

Covers Gaussian random variables, affine transformations, and linear systems driven by Gaussian noise in multivariable control.

Linear Systems: Stability and Solutions

Explores stability and solutions of linear systems in continuous and discrete time.

Linear Systems in 2D: Stability

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

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.