Lectures related to State-Space Representation: Structure Theorem

Observability and Controllability

Explores observability and controllability in linear systems, emphasizing the significance of input decoupling for observability.

State-Space Representation: Controllability and Observability

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

State-Space Representation: Basics & Transformations

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

Controllability and Observability

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

Characteristic Polynomials and Similar Matrices

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

Singular Value Decomposition: Applications and Interpretation

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

Linear Algebra: Reduction of Linear Application

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

Observer Design

Covers the design of observers in control systems and the computation of state feedback controllers.

Controllability and Reachability

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

Stability: Poles, Zeros, and Control

Covers stability, poles, zeros, and control in dynamic systems, emphasizing the importance of observability.

State Space Control: Discrete Systems

Explores the shift from continuous to discrete control systems, focusing on the challenges and benefits of digital implementation.

The Matrix: The Question That Drives Us

Explores the central question that drives individuals to seek the truth.

Linear Algebra: Matrices and Linear Applications

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

Matrix Eigenvalues and Eigenvectors

Covers matrix eigenvalues, eigenvectors, and their linear independence.

Control Theory Fundamentals

Introduces control theory fundamentals, including controllability and invertibility of systems.

Multivariable Control: Weight Design and Stability Analysis

Explores weight design and stability analysis in multivariable control systems, emphasizing Lyapunov theory and LQR stability.

Built-In Self-Test (BIST): Techniques and Implementations

Explores Built-In Self-Test (BIST) techniques in VLSI systems, covering benefits, drawbacks, implementation details, and the use of Linear Feedback Shift Registers (LFSRs) for test pattern generation.

Stability and State Feedback

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

Bode Diagram Synthesis

Covers the synthesis in the Bode diagram, dynamic controls, and the link between the Bode and Nyquist diagrams.

Characterization of Invertible Matrices

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