Extended root-locus technique for design of linear multivariable feedback systems

The root-locus-approximation procedure is extended to provide for the complex-plane analysis of equations which contain a term quadratic in the variable parameter in addition to the usual linear term. Such an extension will have many applications; in the paper, a discussion is given concerning the design of linear time-invariant multivariable feedback systems. It is shown that, particularly for 2-input/2-output problems, where the algebra involved in obtaining the equations to be analysed remains fairly simple, much useful information is available by straightforward hand calculation. Brief suggestions are given for further generalisations of the techniques (inclusion of a cubic gain term etc.)