Kind of Simple but its bugging me?

[Bugzy]

What will be the derivative of sat function where lets say y=-2x1-3x2-5x3.
or in general what will be the derivative of a saturation function.

Thanx in advance.

 

[v_c]

Is the saturation function you are described given by
\[sat(x) = x, \,\,\, -1 \le x \le 1\]
\[sat(x) = 1, \,\,\, x > 1\]
\[sat(x) = -1, \,\,\, x < -1\]

If this is true, then the derivative would be zero in the regions >1 and <-1
and 1 in regions between -1 and 1. For your case I am guessing that
derivative of \[sat(-2x_1-3x_2-5x_3)\] would be 0 if \[-2x_1-3x_2-5x_3 > 1\] and \[-2x_1-3x_2-5x_3 < -1\].

I am not sure about the region \[-1 \le (-2x_1-3x_2-5x_3) \le 1\], perhaps all the partial derivatives with respect to \[x_1, x_2, x_3\] in this region should equal 1.

Best regards,
v_c

 

[Bugzy]

Thanx