On behavior of root loci of uniform and circulant multivariable control systems

In this paper, new significant features of the root locus of the uniform and circulant multiple-input multiple-output systems are presented. It is shown that these multiple-input multiple-output systems have root loci branches that simultaneously possess both the properties of root loci and complimentary root loci of common single-input single-output systems irrespective of the feedback sign. A special attention is devoted to the root locus of uniform and circulant multiple-input multiple-output systems that do not have strictly proper transfer functions. For these systems, it is shown that some branches of the multivariable root loci can pass through infinity for certain finite values of the system gain.