lecture 22

lecture 22 - Design in State Space Controllability Complete...

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1 Design in State Space Controllability Complete state controllability: A control system is controllable if every state variable can be controlled in a finite time period by some unconstrained control signal. It is possible to transfer the system from any arbitrary initial state to any desired state. If the system is completely state controllable, then poles of the closed-loop system may be placed at any desired location by means of state feedback through an appropriate state feedback gain matrix.
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) ( ) ( ) 1 ( k Hu k Gx k x + = + = + + + + = + + + = + = + + = + = + = ) 0 ( . . . ) 2 ( ) 1 ( ] .... [ ) 0 ( ) ( ) 1 ( ... ) 1 ( ) 0 ( ) 0 ( ) ( ...... ) 2 ( ) 1 ( ) 0 ( ) 0 ( ) 2 ( ) 2 ( ) 3 ( ) 1 ( ) 0 ( ) 0 ( ) 1 ( ) 1 ( ) 2 ( ) 0 ( ) 0 ( ) 1 ( 1 2 1 2 3 2 u n u n u H G GH H x G n x n Hu Hu G Hu G x G n x Hu GHu Hu G x G Hu Gx x Hu GHu x G Hu Gx x Hu Gx x n n n n n Necessary and sufficient condition for complete state controllability:
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lecture 22 - Design in State Space Controllability Complete...

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