Series and parallel D-spectra for multi-input-multi-output linear time-varying systems

In this paper some previously developed series and parallel differential spectral concepts for scalar linear time-varying (LTV) systems are extended to some subclasses of multi-input-multi-output (MIMO) LTV systems. The extension is facilitated by the new concepts of differential determinant and differential adjoint matrix introduced herein, which are natural extensions of the familiar concepts of determinant and adjoint matrix to a noncommutative differential ring. Explicit matrix fractional representations are obtained for the subclasses of MIMO LTV systems for which the new results are applicable. The new results have important applications in the analysis and control of MIMO LTV systems.