1.1 Consider a closed loop feedback control system with a characteristic equation given by a second order polynomial (quadratic equation) as follows:

By using general feedback loop stability criterion, find the general criteria or formulae for testing the stability of the above process and answer the following questions:

1. Under which condition will the roots of the characteristic equation are real and how will you assess the stability of the process. State the conditions required for the stability in this case. [6]
2. When will the roots of the characteristic equation become complex and how will you assess the stability of the process. State the conditions required for the stability in this case. [6]
3. Use the testing criteria to assess whether the system below is stable or not. [6]

1.2 Given the characteristic equation:

Determine the stability by the Routh criterion. [7]