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5173 fall 2009 HW08

# 5173 fall 2009 HW08 - observer canonical form for the...

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EEL5173 Signal and System Analysis Fall 2009 HW # 8 Due 10/28/2009 1. The state-space model of a DT system is given as follows: ) ( 0 1 1 ) ( 3 2 0 1 1 0 2 4 0 ) 1 ( k u k x k x + = + r r [] ) ( 2 0 1 ) ( k x k y r = Determine the reachability and the observability of the system. 2. The state-space model of a CT system is given as follows: ) ( 1 3 0 ) ( 0 0 0 1 1 1 1 2 1 t u t x dt x d + = r r [] x y r 1 1 1 = Determine the controllability and the observability of the system. 3. For the system shown, obtain the state-space model of the system by using the
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Unformatted text preview: observer canonical form for the subsystem on the left and using the controller canonical form for the subsystem on the right. When is the system both controllable and observable? Find the transfer function of the system if the system is either uncontrollable or unobservable. 10 6 ) ( 3 2 + + + s s b s u ( t ) w ( t ) y ( t ) ) ( ) ( 4 a s s b s + +...
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