Multivariable Control: System Theory and Linear Systems

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LTI Systems Properties

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

Discrete Systems Analysis: Z-Transform and System Properties

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

Dynamics of Discrete Systems

Covers the dynamics of discrete systems and the concept of orbits in Riemann varieties.

Observability and Controllability

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

Linear Systems: Equilibria and Stability

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

Dynamical Systems: Laplace Transform

Covers the Laplace transform, transfer functions, and properties of common functions in dynamical systems.

Kalman Filter: State Space Models

Introduces the Kalman Filter for estimating the state of a dynamic system from noisy measurements, covering prediction, updating, and filtering steps.

Multivariable Control: Eigenvalue Assignment and Disturbance Estimation

Discusses closed-loop eigenvalue selection and disturbance impact in multivariable control systems.

Sparse Matrices in Multivariable Control

Explores sparse matrices in multivariable control, emphasizing projection computation and PGD convergence.

Observability and Duality

Delves into the observability of LTI systems, covering controllability, duality, and observability tests.