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 demonstratein this paper that at the heart of the extensions canied out Kere lies the result that if a stable multivariable, linear time varying system is stable under aU scalar constant, positive feedback gains, then it has a well defined squam root. The existence of this squam root is demonstrated through a consbuctive Newton-Rapbson based algorithm. The various extensions provided here though diierent '. A closed-'oop configurat'on. in form fmm their linear time invariant scalar counterparts, do recover these as special cases. where the superscript H denotes the Hermitian trans