Robust Pole Assignment in a Problem of State Observer-based Modal Control

Abstract

The results of the development of an approach for the robust pole assignment based on the fulfillment of the Rouche's theorem conditions for a linear time-invariant single-input single-output system with system matrix parametric uncertainty and full-order state observer-based modal control are presented. The proposed approach allows to determine the minimum value of the geometric mean root of the desired characteristic polynomial of a system with a modal controller for given types of polynomials of a system with a modal controller and an observer, as well as the ratio of the roots values of these polynomials and a characteristic index determining the shape of the pole scatter domain, its size and location relative to the imaginary axis, as well as the minimum achievable dynamics performance, at which bounded parametric perturbations of the system matrix do not bring the poles of the closed-loop system beyond the boundaries of a certain domain of the complex plane.