Fundamental limitations imposed by RHP poles and zeros in SISO systems

Abstract

Establishes limitations on the impulse response of an LTI system based on the open-loop poles and zeros located in the convergence region of the closed-loop transfer function. Using the definition of Laplace transform, it is shown that time-domain integral constraints have to be satisfied by the impulse response of the SISO stable system and that the maximum value of impulse response has some lower bounds according to the achievable settling time of the system. Also, it shows the reason why it is very difficult to control the system with open-loop RHP (right half plane) poles or zeros using the unity-feedback scheme in the view of small impulse response. These results can be used to determine a priori whether desired design specifications axe achievable or not.