Generalized Bode envelopes and generalized Nyquist theorem for analysis of uncertain systems

Abstract

AbstractThis work is concerned with analysis of uncertain control systems, with regard to clustering of poles inside a simple symmetric bounded contour. We present and use the generalized Bode envelopes, generalized Mikhailov theorem, and the generalized Nyquist theorem for the simultaneous analysis of stability and quality of transient response of uncertain systems. Our results allow one to determine the number of open‐ and closed‐loop poles inside the given symmetric simply connected contour, for the entire uncertain family. The proposed method is computationally efficient and appropriate for solving complex control analysis problems, as evidenced in the examples. Copyright © 2010 John Wiley & Sons, Ltd.