Hankel Singular Values and LQG Characteristic Values of Discrete-Time Linear Systems in Cascade with Inner Systems

Recent results have shown that, for continuous-time systems obtained by cascading an asymptotically stable system with an inner system, the first $n$ Hankel singular values are greater than or equal to those of the original system. Similarly, cascading a system in minimal form with an inner system, the same property holds for the linear quadratic Gaussian (LQG) characteristic values. In this article, we consider the discrete-time case and demonstrate that the property also holds for these systems. A very important consequence stemming from these results is that the Hankel singular values and the LQG characteristic values of input-delayed discrete systems are greater than or equal to those of their zero-delay counterpart.