Lectures related to Lyapunov stability

Introduction to Dynamical System

Introduces dynamical systems, equilibrium points, stability, vector fields, phase plots, and Lyapunov stability.

Equilibrium Stability Analysis

Explores equilibrium stability analysis, emphasizing the importance of stability calculations for balanced systems.

Circle Criterion: Stability and Nonlinearity

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

Stability in Feedback Systems

Explores BIBO stability in feedback systems, covering criteria, Nyquist criterion, and system sampling impact.

Stability of LTI Systems: Equilibria and Lyapunov Theory

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

Stability and State Feedback

Covers BIBO stability, Lyapunov stability, state feedback, and eigenvalue assignment.

Lyapunov Stability and Linearization

Explores Lyapunov stability, linearization, and system stability examples.

Lyapunov Stability and Chebyshev Inequalities

Explores Lyapunov stability and Chebyshev inequalities in system analysis and control design.

Chaos and Lyapunov Exponents: Analyzing Predictability

Covers Lyapunov exponents, chaos measurement, and perturbation analysis in dynamical systems.

Dynamical Systems: Maps and Stability

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Non-linear Control: Stability Analysis

Explores linearization, state representations, and stability analysis using Lyapunov theory and zero dynamics.

Lyapunov II: Stability and Invariance

Explores Lyapunov stability and invariance of dynamical systems through examples and corollaries.

Car following models: Intro to traffic flow modeling

Covers car following models, stability, lane changing, and microsimulation advantages, challenges, and characteristics.

Nyquist Introduction

Introduces the Nyquist criterion to determine system stability and covers BIBO stability and stability conditions.

Lyapunov Stability Analysis

Covers Lyapunov stability analysis, focusing on Lyapunov functions and stability criteria in robotic systems.

Non-linear Control: Lyapunov Method

Covers exercises on the Lyapunov method in non-linear control systems, focusing on stability analysis and Lyapunov functions.

Lyapunov Methods: Stability Analysis

Explores Lyapunov methods for analyzing stability in nonlinear control systems using functions and mechanical analogies.

Networked Control Systems: Stability Analysis and Delay Compensation

Explores stability analysis and delay compensation in networked control systems, emphasizing the importance of compensating for known delays.

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.

Lyapunov Stability in Dynamical Systems

Covers Lyapunov stability in dynamical systems, focusing on global asymptotic stability and practical implementation through semidefinite programming.