Unstable Closed Loop Poles

I have a plant transfer function gs which is stable on its own but the feedback loop is unstable because a pole appears on the right hand side of imaginary axis. How can I go about making system stable? I'm trying to make a controller similar to what's shown below with a lag compensator but I think I need to remove the unstable pole first.

gs = tf([-15.06 14.3 0.384], [1 2.383 8.791 0.2651 0.09111]) % plant transfer function

CLTF = feedback(gs,1) % results in closed loop poles that are unstable

Answer 1

[Net Fre]

Using the rlocus function, you can see that up to a certain value of C (around 0.4 in your case) your closed loop will still be stable. Notice that the closer you get to that value your system will be closer to being unstable and will oscillate more.

Therefor you can start your controller design with a lower gain, such as:

CLgain = 0.25;
CLTF = feedback(CLgain*gs,1)

and try moving on from there.