Modern control and state space representation

Explore state space concept for linear systems, deriving x_{k+1}=A x_k + B u_k and y=C x_k to model multiple-input, multiple-output systems from differential equations.

Demonstrate obtaining a state-space representation from a system with derivative inputs using block diagrams of integrators and summers, and derive the state equations and A, B, C, D matrices.

Explore deriving state-space representations from circuit differential equations, transforming them into matrix form for single and multi-input systems, with emphasis on state variables, inputs, and outputs.

Convert a transfer function to a state-based representation using cross multiplication and time-domain derivatives, then build state equations and a block diagram in CCF.

Explore cascade realization and parallel realization to convert a transfer function into state-space form using canonical control form and partial fraction methods.

Explore cascade realization to convert a transfer function into a state-space representation, derive A, B, C, D from the cascade with integrators and feedback, and prepare for state-space control.

Explore controllability and observability in state-space models, using the controllability matrix [B, AB, ..., A^{n-1}B] and the observability criterion with C^T, (CA)^T, ..., (CA^{n-1})^T, noting B encodes mass, inertia, and stiffness.

Apply state feedback to achieve a closed-loop system with A minus B K, and analyze stability via the eigenvalues of this matrix using the characteristic equation.

Delve into the generalized Gendron method to derive eigenvalues and eigenvectors, and apply the same approach to state feedback and output feedback, emphasizing controllability, poles, and handling repeated eigenvalues.

Explore computing eigenvalues and eigenvectors for a state-space system by applying the general method to matrices A and B, handling underdetermined equations with delta variables.

Learn how to derive output feedback from a state-space representation and compare it with state feedback, using generic method and A, B, C, D matrices, while noting controllability and observability.