Solving Lyapunov Equation: Need Help Finding Q

[Firepanda]

I had a thread earlier on the notation but it hasn't really helped me progress on the question.

I'm really confused on how to start this, am I expected to find Q myself? As in choose any random Q?

I need the Q to maximise rho, and so I think I need to find a Q where q₁ is as large as possible?

I know how to find P and ||P|| using matlab, but it's finding Q that I cannot do!

There are zero examples of this in my notes, it's just all theory and I'm really clueless.

Any help would be great.

Thanks

 

[mighty2000]

Hello,

Thank you for reaching out for help with your question. I understand that sometimes the notation and theory can be confusing, but it's important to take some time to fully understand the problem before attempting to solve it.

In this case, it seems like you are trying to find the optimal Q that will maximize the value of rho. In order to do this, you will first need to understand the variables and their meanings. Q represents a matrix, and q1 represents the first column of that matrix. So, you are correct in thinking that you need to find a Q where q1 is as large as possible.

To do this, you will need to use some mathematical techniques such as optimization or linear algebra. These techniques will help you find the optimal values for Q that will maximize rho. It is not expected for you to choose a random Q, but rather to use mathematical methods to find the best Q.

If you are having trouble finding examples in your notes, I suggest reaching out to your professor or classmates for help. They may be able to provide you with some practice problems or additional resources to better understand the concept.

I hope this helps and good luck with your question. Don't hesitate to ask for help if you continue to struggle. Remember, as a scientist, it's important to fully understand the problem before attempting to solve it.