Generalized Nyquist Criterion and Generalized Bode Diagram for Analysis and Synthesis of Uncertain Control Systems

Uncertainties in control systems models often have to be taken into account in their analysis and/or design. Negligence of such uncertainties is often unjustifiable and is done only due to lack of methods to treat the uncertainties. The presented work is concerned with analysis and design of interval uncertainty control systems, with regard to clustering of poles inside a simple symmetric bounded contour ¿. We extend the well known Nyquist and Mikhailov stability theorems to ¿ - stability tests of uncertain systems, defined by their generalized Bode envelopes. Also, using generalized definitions and theorems we solve the design problem of a controller which ensures clustering of closed loop poles of an interval uncertain family of transfer functions inside such prescribed ¿ -region.