A study on square root control-systems

Starting with the simplest case of an analogue square root control-system, we extend the idea to the discrete-time case and ultimately the multivariable discrete-time case. Several new results then emerge from the multivariable work. A nonlinear system is designed to take the square root of an arbitrary square matrix. The matrix can have real or complex values and an analysis of stability is reached by using matrix calculus and nonlinear theory. The root-locus of the multivariable system exhibits straight-line characteristics which has not been observed before and to achieve stability we introduce the concept of a complex step-size (or gain) in a recursive square root algorithm.