# Doubt on behaviour of frequency responce of a system

I am doing loop shaping using $$H_{\infty }$$ approch, and I have a plant with an unstable pole:

G = 10/((s+10)*(s-1));
K1 = 4*(s+1)/s;


where G is the plant, and K1 is the controller. I am trying to do a confrontation between the approch with $$H_{\infty }$$ and the one without, in particular I am placing a weight only for the sensitivity function, and designing a controller using the mixed sensitivity design.

What I get if I plot the frequency response of the system in the two cases is the following: in which the yellow line is the frequency response of the system in which I applied the $$H_{\infty }$$ and the red line is the one in which I used G and K1 as they are, so without mixed sensitivity and weights.

What I don't understand is why the yellow line has this strange behaviour, while the red line decrease smoothly.

I see that the bandwidth of the yellow line is lower the the other one, so maybe this fact is due to the fact that I have a RHP pole which imposes a lower limitation on the bandwidth of the system. But, if I plot the sensitivity functions of these two systems, I have: so the yellow line behaves better with respect to disturbance rejection with respect to the red line, as expected.

I don't understand how to interpret the behaviour of the yellow line of the complementary sensitivity function.

Can somebody help me?