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# FL10quiz10 - t ≥ 0 d How do you explain the zero-state...

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ESE 351 Quiz 10 Name: 10/5/10 Sections 6.3–6.7 Let A be an n × n square matrix and let x 0 be an n -dimensional vector. a) Consider the following representation of a system: d dt x ( t ) = Ax ( t ) + Bu ( t ) , x ( t 0 ) = x 0 , y ( t ) = Cx ( t ) + Du ( t ) . The complete response y ( t ) of this system consists of two parts: the zero-state response y zs ( t ) and another term. What is the name given to this second term? b) Consider x ( k +1) = Ax ( k ), k 0, with x (0) = x 0 . What is the solution x ( k ) for k 0? c) Consider d dt x ( t ) = Ax ( t ), t 0, with x (0) = x 0 . What is the solution x (
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Unformatted text preview: t ≥ 0? d) How do you explain the zero-state response of a system? Be sure to explain the meaning of zero-state in English. e) The following is given as the solution for the discrete-time system in our classnotes: x ( k ) = A k-k x + k-1 X ‘ = k A k-‘-1 Bu ( ‘ ) . Find the solution for x ( k + 1) = Ax ( k ) + Bu ( k ) , x (0) = x . Hint: You need to specialize k ....
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