Adaptive PD algorithm


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I am simulating a PD for a quadrotor, where I developed following adaptive PD algorithm:

Kp(t+1) = Kp(t) + e(t)*alpha
Kd(t+1) = Kd(t) + e(t)*alpha
e(t) is the error function of the simple difference between a desired angle and current angle of the quadrotor.

Does this adaptive PID algorithm make sense? I am updating with 0.1 seconds of frequency. How can I test the stability of this function, please?
1. You need define range of Kp and kd (i.e. low and high limits) as well.

2. You must take absolute value of e(t)

3. Changing of kd is effective for dynamics but not for steady state

I do not agree about using absolute value in this case, as this would imply that Kp and Kd keep always growing. Could I check the stability of this with Lyapunov discrete theorem?