Lectures related to Non-linear Control: Stability Analysis

Stability of ODE

Explores the stability of Ordinary Differential Equations, focusing on solution dependence, critical data, linearization, and control of nonlinear systems.

Introduction to Nonlinear Systems Control

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

Exact Linearization: Earth Dynamics and Stabilization

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

Passivity, Stability and Circle Criterion

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

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.

Circle Criterion: Stability and Nonlinearity

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

Advanced Numerical Analysis: Space Discretization

Explores advanced space discretization techniques in numerical analysis for solving differential systems efficiently and accurately.

MHD Stability and Equilibrium

Explores MHD equilibrium and stability, emphasizing energy considerations for determining stability.

Nonlinear Dynamics: Stability and Chaos

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

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 Reachability in Multivariable Control

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

Stability in Feedback Systems

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

System Identification and Stability

Explores system identification, stability criteria, and challenges in stabilizing cameras on moving platforms.

Nonlinearity: Methods and Examples

Explores nonlinearity in numerical flow simulation, covering linearization methods and practical examples.

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.

Systems: Properties and Behavior

Covers the fundamental properties of systems in discrete and continuous time domains.

Stability: General Notions

Covers the general notions of stability in linear systems and the relationship between bounded inputs and bounded outputs.

Stability of periodic solutions of continuous-time systems

Explores the stability of periodic solutions in continuous-time systems using the logistic map and the van der Pol oscillator.

Linear Systems: Stability and Solutions

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