Difference between open and closed loop systems? Impact of RHP on stability? Difference between compensator and filter?

I applied for the Control Systems stream. The last stage was the on-site interview after 2 HR rounds and one technical round. Technical Round: The questions were divided into clear sections just like the telephone one. They expected you to know the answer properly and answer most of the questions. I don't remember all of them, sorry. - Find eigenvalues and eigenvectors of a 2x2 matrix - Find the maximum area of a rectangle under a curve You have to write the expression for y from the equation of the curve. Area =x*y. Differentiate, equate to zero and find the value of x for which the area is maximum. Then take the second derivative and check if the value of the function is <0 - Write a recursive function to determine the factorial/fibonacci numbers - Write pseudo code for any sorting algorithm - Write an algorithm to draw a section of an arc if the topmost is a point (y,0) - Some inheritance questions - They gave me a snippet of a code that copies one string to another and asked me what the function does - Find the bug in a piece of code. - Pointer questions like *++q and ++*q - Draw the responses of differently damped systems for a 2nd order linear system - What happens if there are zeros in the system - Lead-lag compensators - Lyapunov stability - Controllability and Observability HR and manager rounds - How are you with working in teams? - How would your supervisor describe you? - What do you think your supervisor thinks your main weakness are? - Can you handle multiple responsibilities? - What is your prefered supervision style? - If you could not do any control systems at all in this role, how will you handle it? Will you be okay with it?