User:Egm6321.f10.team2.oztekin/sandbox

Same observation for Bryson, A.E., and Ho, Y.C Book's Eq.
The solution of SC_N1_ODE is given in the book as follows ;


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$$  \displaystyle X(t)=\phi (t,t_{0})X(t_{0})+\int_{t_{0}}^{t}\phi (t,t_{0})B(\tau )U(\tau )d\tau $$     (N)
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So we can see that


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$$  \displaystyle \phi (t,t_{0})_{n\times n}=expA(t-t_{0})_{n\times n} $$ (N)
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$$  \displaystyle \dot{X(t)}=A\phi (t,t_{0})x(t_{0})+\frac{\mathrm{d} t}{\mathrm{d} t}\phi (t,t)B(t)U(t)+\int_{t_{0}}^{t}\frac{\mathrm{d} }{\mathrm{d} t}\phi (t,\tau )B(\tau )U(\tau )d\tau $$     (N)
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$$  \displaystyle \dot{X(t)}=A\phi (t,t_{0})x(t_{0})+B(t)U(t)+A\int_{t_{0}}^{t}\varphi (t,\tau )B(\tau )U(\tau )d\tau $$     (N)
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We concluded that
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$$  \displaystyle \dot{X}(t)-AX(t)=B(t )U(t) $$     (N)
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Since zou has drived comprehensively in his discussion page we concluded briefly just to show that book's equation yields exactly the same equtiation we drived in our lecture.