ROBUSTNESS OF UNIFORM CONTROL SYSTEMS WITH MULTIPLICATIVE UNCERTAINTIES
2024
This paper aims to develop simple graphical tests for analyzing stability robustness of uniform control systems with respect to multiplicative uncertainties. The uniform systems are multi-input multi-output (MIMO) feedback control systems having identical transfer functions of separate channels and rigid cross-connections described by a square numerical matrix. The exposition is based on the method of characteristic transfer functions, which allows reducing the stability analysis of an interconnected MIMO system with and outputs to the analysis of fictitious independent systems with one input and one output. The proposed robustness tests are in the form of “forbidden” circles on the complex plane of characteristic gain loci of the open-loop uniform system. A numerical example illustrating application of the tests to the analysis of stability robustness of a three-dimensional uniform system is given.