New result on PID controller design of LTI systems via dominant eigenvalue assignment

This note considers the problem of assigning the dominant eigenvalues of a linear time-invariant (LTI) system to the desired positions by using proportional–integral–derivative (PID) controllers. The procedure is based on first setting some rightmost eigenvalues of the system at the desired positions and then guaranteeing the dominance of those rightmost eigenvalues by using the generalization of the Hermite–Biehler Theorem. It is worth pointing out that this work aims to ascertain the gains of PID controllers in a straightforwardly computational way which plays an important role in practical applications.