Lectures related to Multivariable Control: Equilibria and Stability Analysis

Linear Systems: Equilibria and Stability

Explores linear systems' equilibria, stability, and modes, including Lyapunov stability and exponential stability.

Multivariable Control: Eigenvalues and Modes

Explores eigenvalues and modes in multivariable control systems, focusing on their analysis and behavior.

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

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Controllability and Reachability

Explores reachability and controllability in multivariable control systems, discussing tests, proofs, and their implications.

Multivariable Control: System Theory and Applications

Covers system theory, classic feedback control, and applications in green building and natural gas refrigeration plants.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Modes and Stability of LTI Systems

Explores the analysis of free states and modes in multivariable control systems, emphasizing stability properties and practical examples.

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Multivariable Control: System Theory and Linear Systems

Introduces the basics of multivariable control, focusing on system theory and linear systems.

Stability Analysis: Linear Systems

Explores stability analysis in linear systems, emphasizing eigenvalues, eigenvectors, and stable manifolds.

Multivariable Control

Covers Gaussian random variables, affine transformations, and linear systems driven by Gaussian noise in multivariable control.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Reachability and Controllability of LTI Systems

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

Introduction to Multivariable Control

Covers the basics of multivariable control, including system modeling, temperature control, and optimal strategies, emphasizing the importance of considering all inputs and outputs simultaneously.

Linear Systems: Stability and Solutions

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

Exact and Approximate Sampling in Multivariable Control

Explores exact and approximate sampling in multivariable control systems, discussing stability, eigenvalues, and system properties.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Multivariable Control: System Theory and Linear Systems

Introduces multivariable control, covering system theory, linear systems, and time discretization.

Eigenvalues and Fibonacci Sequence

Covers eigenvalues, eigenvectors, and the Fibonacci sequence, exploring their mathematical properties and practical applications.