Lectures related to Linear Systems Control: Fundamentals and Applications

Covers the basic concepts of control theory and the selection of optimal controls.

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

Controllability and Observability

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

Stability of ODE

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

State-Space Representation: Structure Theorem

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

Control Theory Fundamentals

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

Observability and Controllability

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

Linear Control Systems

Covers the reduction of complex systems to linear situations and controllability conditions.

State-Space Representation: Controllability and Observability

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

Linear Algebra: Matrices and Vector Spaces

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Nonlinear Model Predictive Control

Explores Nonlinear Model Predictive Control, covering stability, optimality, pitfalls, and examples.

Infinite-Horizon LQ Control: Solution & Example

Explores Infinite-Horizon Linear Quadratic (LQ) optimal control, emphasizing solution methods and practical examples.

Linear Quadratic Optimal Control: Theory and Applications

Explores Linear Quadratic optimal control theory, covering FH-LQ and IH-LQ problems and the importance of observability in control systems.

Linear Systems: Fundamentals and Applications

Explores the power of linear systems in control theory and data science.

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Linear Transformations: Matrices and Bases

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.