Lectures related to Discrete-time Systems and Lyapunov Theory

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.

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.

Stability and Eigenvalues of LTI Systems

Explores stability and eigenvalues of LTI systems, reachability, and controllability of dynamical 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.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Introduction to Dynamical System

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

Stability and Reachability in Multivariable Control

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

LTI Systems Properties

Covers the properties of Linear Time-Invariant (LTI) systems and their implications.

Reachability and Controllability of LTI Systems

Explores reachability and controllability of LTI systems, discussing testing methods, properties, definitions, and their relationship.

Z-Transforms: Poles and Zeros

Explores Z-Transforms, Poles, Zeros, and their applications in discrete-time systems and Linear Time-Invariant systems.

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.

Networked Control Systems: Protocol-induced Delays and Time-varying Sampling

Explores protocol-induced delays, time-varying sampling, wireless control networks, and system stability.

Discrete Systems Analysis: Z-Transform and System Properties

Explores Z-transform, system properties, and analysis of discrete systems, focusing on stability and transfer functions.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

LTI Systems: Analysis and Properties

Covers the analysis and properties of Linear Time-Invariant (LTI) systems.

Linear Time Invariant Systems: Impulse Response and Convolution

Covers linear time invariant systems, focusing on impulse response and convolution.

Lyapunov Stability in Dynamical Systems

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

Discrete-Time Systems Analysis

Explores Z-transform analysis for discrete-time systems and transfer functions in control systems.

Stability and State Feedback

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

Circle Criterion: Stability and Nonlinearity

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