Derivation step for adaptive backstepping Lyapunov function

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Homework Statement


I can't seem to figure out how this next step of this derivation for equation 2.33 was produced. This is a graduate level textbook on Adaptive Backstepping.
 
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  • Printed text and equations from an adaptive backstepping textbook: controller definitions alpha_1 = -c1 z1 - phi1^T theta_hat1 and update law, Lyapunov function V1 = z1^2/2 + theta_tilde^T Gamma^-1 theta_tilde/2, and the derivative of V1 simplified to -c1 z1^2 + z1 z2.
    lyapunov1.png
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Discussion

In case my question wasnt clear enough, I don't understand how the author produced equation 2.33.
 

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