Lectures related to Introduction to Dynamical System

Dynamical Systems: Equilibrium Points and Stability

Covers dynamical systems, equilibrium points, stability analysis, and phase plots using examples like the pendulum system.

Nonlinear Dynamics: Stability and Chaos

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

Lyapunov Stability in Dynamical Systems

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

Bifurcations: Fold Bifurcation

Covers the concept of fold bifurcation in dynamical systems, focusing on the saddle-mode behavior.

Dynamical Systems: Maps and Stability

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

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.

Dynamical Systems for Engineers

Covers the theoretical basis of linear and nonlinear dynamical systems for engineers.

Stable Estimator of Dynamical System (SEDS)

Explores Stable Estimator of Dynamical Systems (SEDS) for robots, covering stability, modeling, optimization, and limitations.

Small Scale Stability: Gradient Systems

Explores small scale stability in gradient systems, analyzing trajectories and attractors in phase space.

Chaos and Lyapunov Exponents: Analyzing Predictability

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

Stability and Reachability in Multivariable Control

Explores stability, reachability, and controllability in linear systems, emphasizing their significance in system analysis.

Mathematical Modeling in Chemistry and Biology

Covers mathematical modeling in chemistry and biology, including chemical reactions, enzymatic kinetics, and population dynamics.

Linear Systems in 2D: Stability

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

Lyapunov Stability and Chebyshev Inequalities

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

Mechanical Energy: Equilibrium and Oscillations

Explores mechanical energy, equilibrium, and small oscillations in rectilinear motion.

Lyapunov Stability Analysis

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

Lyapunov Stability: Theory and Applications

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

Small Scale Stability: Equilibrium Point

Covers small scale stability at equilibrium points in dynamical systems for engineers.

Lyapunov II: Stability and Invariance

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

Small Scale Stability: Equilibrium Point

Discusses stability analysis of equilibrium points in dynamical systems.