Develop a function which takes consideration of current state $x$ and first time derivative of the state $\dot{x}$

Question

I would like to develop a function $f$ which take consider of current state $x$ and the first time derivative of state $\dot{x}$ for decision making $\alpha \in [0,1]$ (Whether the system behave good ($\alpha = 1$) and the system behaves bad $\alpha = 0$).

$\alpha = f(x,\dot{x})$

Here are some functions $f$ I could think about:

1. $\alpha = min(x,\dot{x})$
2. $\alpha = x \times \dot{x}$
3. $\alpha = \lambda \times x + (1 - \lambda) \times \dot{x}$

My math foundation is bad. I would appreciate anyone could suggest me more sophisticated function $f$.