Control-Lyapunov function: Difference between revisions

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u= m(1+q^2)(\ddot{q}_d + \alpha \dot{e}+\frac{\kappa}{2}r )+K_0q+K_1\dot{q}+b\dot{q}
</math>
with <math>\kappa</math> and <math>\alpha</math>, both greater than zero, as tunable parameters
 
This control law will guarentee global exponential stability since upon substitution into the time derivitive yields, as expected