Balanced Truncation of $k$-Positive Systems

This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has or less, then it is totally positive ($\infty$-positive), meaning a sum first lags. can be understood as bridge between two known results: property first-order ($k=1$), and preserves state-space symmetry. It provides broad class systems where guaranteed in minimal internally system.