MIT6_241JS11_lec22

MIT6_241JS11_lec22 - 6.241 Dynamic Systems and Control...

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Unformatted text preview: 6.241 Dynamic Systems and Control Lecture 22: Balanced Realization Readings: DDV, Chapter 26 Emilio Frazzoli Aeronautics and Astronautics Massachusetts Institute of Technology April 27, 2011 E. Frazzoli (MIT) Lecture 22: Balanced Realization April 27, 2011 1 / 10 Minimal Realizations We have seen in the previous lectures how to obtain minimal realizations from non-minimal realizations (i.e., keeping the reachable and observable part from the Kalman decomposition), and also algorithms to construct minimal realizations of a transfer functions. Minimal realizations are unique up to similarity transformations. However, there are some realizations that are more useful than others, for a number of reasons Kalman decomposition Standard forms Canonical forms . . . In this lecture we will consider what is known as balanced realization . E. Frazzoli (MIT) Lecture 22: Balanced Realization April 27, 2011 2 / 10 The Hankel Operator Consider for simplicity a discrete-time system G with state-space realization ( A , B , C , D ), and transfer function H ( z ), with impulse response ( H , H 1 , H 2 ,... ). How do outputs at time steps k ≥ depend on inputs at time steps k < 0? ⎤ ⎡ H H 1 H 2 ··· ⎤ ⎡ ⎤ ⎡ y [0] u [ − 1] u [ − 2] ⎥ ⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎢ ⎣ H 1 H 2 ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎦ y [1] · · · H 2 ....
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This note was uploaded on 01/12/2012 for the course ECE 6.241j taught by Professor Prof.emiliofrazzoli during the Spring '11 term at MIT.

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MIT6_241JS11_lec22 - 6.241 Dynamic Systems and Control...

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