Lectures related to Observability and Controllability

Covers the structure theorem for state-space representations and companion forms.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores state-space representation, controllability, observability, and regulator calculation using the Ackermann method.

Covers controllability and observability in linear systems, discussing necessary conditions and implications of unimodular matrices.

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

Covers the Singular Value Decomposition (SVD) in detail, including properties of matrices and system linearity.

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

Covers the basics of state-space representation and explores transformations to different forms.

Explains linear independence, basis, and matrix rank with examples and exercises.

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Covers direct methods for solving linear systems in numerical analysis.

Covers linear systems, diagonal and triangular matrices, and LU factorization.

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

Introduces Convex Optimization notation, convex functions, vector norms, and matrix properties.

Covers the concept of balanced realization in the SISO case, focusing on system observability and controllability.

Covers matrices, linear applications, vector spaces, and bijective functions.

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explores matrix rank, subspaces, and their role in solving linear systems of equations.

Explores the properties of invertible matrices, including unique solutions and linear independence.

Explores the Rank Theorem in linear algebra, covering matrix properties and determinants.