Math Problem Statement

Determine whether the system is observable and/or controllable with given matrices for system dynamics and output.

Solution

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TUTORIAL 6

State feedback controllers and digital control systems

  1. Determine whether the system is observable and/or controllable:
\begin{bmatrix} -1 & 1 \\ 1 & -1 \end{bmatrix} x + \begin{bmatrix} 1 \\ 1 \end{bmatrix} u$$ $$y = \begin{bmatrix}1 & 0\end{bmatrix} x$$ --- Would you like help determining the observability and controllability of this system?

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Control Systems

Formulas

State equation: \dot{x} = Ax + Bu
Output equation: y = Cx

Theorems

Controllability using rank(\[B, AB, A^2B, ..., A^{n-1}B\])
Observability using rank(\[C; CA; CA^2; ...; CA^{n-1}\])

Suitable Grade Level

University Level - Advanced Engineering

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