The square root of linear time varying systems with applications

This paper considers the extension of a number of passive multiplier theory based results, previously known only for linear time invariant scalar systems, to linear time varying (LTV) multivariable settings. The extensions obtained here have important applications to the stability of both adaptive systems and linear systems in general. We demonstrate in this paper that at the heart of the extensions carried out here lies the result that if a stable multivariable, linear time varying system is stable under all scalar constant, positive feedback gains, then it has a well defined square root. The existence of this square root is demonstrated through a constructive Newton-Raphson based algorithm. The various extensions provided here though different in form from their linear time invariant scalar counterparts, do recover these as special cases