Lectures related to Lyapunov function

Circle Criterion: Stability and Nonlinearity

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

Lyapunov Stability and Chebyshev Inequalities

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

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

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

Non-linear Control: Lyapunov Method

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

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: Lyapunov Stability and LQR Theorems

Explores Lyapunov stability, LQR theorems, and discounted LQR in multivariable control.

Lyapunov Stability: Convex Optimization

Covers Lyapunov stability in convex optimization and its implementation through trajectory plots.

Chaos and Lyapunov Exponents: Analyzing Predictability

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

Lyapunov Stability in Simple Pendulum

Explores Lyapunov stability theory in the context of a simple pendulum system, demonstrating its application and implications.

Nonlinear Dynamics: Stability and Chaos

Explores fixed point stability, Lyapunov functions, Lotka-Volterra models, and nonlinear dynamics in complex systems.

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.

High Order PDE-Convergence: ADI-Type Integrators

Covers the convergence of high-order PDEs using ADI-type integrators for parabolic problems.

Multivariable Control: Stability and Lyapunov Theorems

Explores multivariable control, optimal laws, and system stability theorems, emphasizing the importance of observability.

Lyapunov Stability Analysis

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

Discrete-time Systems and Lyapunov Theory

Covers the review of linear discrete-time systems and Lyapunov theory, focusing on stability and equilibria.

Lyapunov Methods: Stability Analysis

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

Learning and Adaptive Control for Robots: SEDS & LPV-DS

Explores learning and adaptive control for robots through SEDS and LPV-DS, emphasizing stability, non-linear dynamics, and optimization.

Networked Control Systems: Stability Analysis and Estimation

Covers the analysis and estimation of stability in networked control systems, including the impact of sampling intervals and delays.

Lyapunov Stability: Theory and Applications

Covers the Lyapunov stability theory and its applications in analyzing dynamical systems.