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Lecture 10: Controllability and Observability

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Schedule :: Perspective :: Transfer Functions :: Laplace Transform :: Poles and Eigenvalues :: Time Domain :: Linear Transformations :: Special Transformation :: Controllability :: Discrete-Time

\begin{example}
Cascade representation
\begin{displaymath}H_1(s) = \frac{1}{s-1...
...ite state equations. Second state variable not {\bf controllable}.
\end{example}
Note that in both cases, the end-to-end transfer function hides some information -- there is cancellation there. The transfer function provides a potentially inadequate representation of what is going on. In the general case, let us write
\begin{displaymath}\zbfdot = \Lambda \zbf + \Bhat \fbf \end{displaymath}


\begin{displaymath}\ybf = \Chat \zbf + \Dhat \fbf
\end{displaymath}

where $\Lambda$ is a diagonal matrix -- all the modes uncoupled. If there is a row of zeros in $B$ , then $\fbf$ has no influence on the corresponding state variable. That variable is said to be uncontrollable . If there is a column of zeros in $\Chat$ , then the corresponding state variable is said to be unobservable . For many purposes, systems should be both controllable and observable.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 08). Lecture 10: Controllability and Observability. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/10_7node7.html. This work is licensed under a Creative Commons License Creative Commons License