deletions | additions       diff --git a/Control Theory.tex b/Control Theory.tex  index c10ae67..2a95125 100644  --- a/Control Theory.tex  +++ b/Control Theory.tex 
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If the system is LTI (linear and time-invariant), then matrices $A,B,C,D$ will be time-independent. Our hope is to formulate the nonlinear spectroscopy problem in a form suitable for control theory analysis.  Our observation $P_3(t)$ can be interpreted as $\v{y}(t)$ as shown above. In particular, $C(t) = \left( \begin{array}{c} 0 \begin{matrix}(0  & 0 & 0 & F \end{array} \right)$ F)\end{matrix}$  and $D(t) = \v{0}$. Can the time dependence within $H(t)$ be modeled as input $\v{u}(t)$ to the system? In general, $H(t) = H_0 + E(t) \cdot \mu$. Let us define superoperators $A_0, A_1$ such that $A(t) = A_0 + E(t) \cdot A_1$. By linearity of the commutator, applying $A_0$ (in operator form) can behave as $A_0 \cdot = \frac{-i}{\hbar}[H_0,\cdot]$, and applying $A_1$ (in operator form) can behave as $A_1 \cdot = \frac{-i}{\hbar}[\mu,\cdot]$.