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Matrix equation, solving for x(t)

  1. Oct 17, 2011 #1
    this comes strait from a text book:
    http://higheredbcs.wiley.com/legacy/college/nise/0471794759/appendices/app_i.pdf
    I am looking at how they obtained (I.24) from (I.25) on page 3 and 4.

    Firstly we have:

    [itex]e^{-\textbf{A}t}x(t)-x(0)=\int{e^{-\textbf{A}t}\textbf{Bu}(\tau)d\tau}[/itex]

    Then this is derived to:

    [itex]x(t)=e^{-\textbf{A}t}x(0)+\int{e^{-\textbf{A}(t-\tau)}\textbf{Bu}(\tau)d\tau}[/itex]

    my question is why does the derived equation have [itex]e^{-\textbf{A}t}[/itex]. I thought it would have been [itex]e^{\textbf{A}t}[/itex] instead. Can someone explain this too me. The text didnt help me.
     
  2. jcsd
  3. Oct 17, 2011 #2

    AlephZero

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    I think there are typos in the first line of equation 25. Some of the minus signs shouldn't be there.

    The statement "where [itex]\Phi(t) = e^{At}[/itex] by defintion" and the equation involving [itex]\Phi[/itex] are correct.

    Just take equation 24 and multiply all the term by [itex]e^{At}[/itex] (note, no minus sign!) to get the correct version.
     
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