deletions | additions       diff --git a/CRM MRAC of a First-Order Nonlinear System1.tex b/CRM MRAC of a First-Order Nonlinear System1.tex  index d4f3897..a0e92b4 100644  --- a/CRM MRAC of a First-Order Nonlinear System1.tex  +++ b/CRM MRAC of a First-Order Nonlinear System1.tex 
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which leads to   \begin{align}  e^{c}=\frac{1}{k^{*}}\frac{km}{s-(am+l)}\tilde{\theta}^T\phi=\frac{1}{k^{*}}M(s)[\tilde{\theta}^T\phi] e^{c}=\frac{1}{k^{*}}\frac{k_m}{s-(a_m+l)}\tilde{\theta}^T\phi=\frac{1}{k^{*}}M(s)[\tilde{\theta}^T\phi]  \end{align}  where $M(s)$ is SPR. Using the MKY-Lemma, we know, that a Lyapunov function exits s.t. the derivative is negative definite. Hence the dynamics of the closed loop errror is asymptotically stable.  %Using Lyapunov's second method with the Lyapunov candidate function