Passivity and practical considerations for the SNMF System

Systems comprised of many subsystems can benefit from reducing the number of inputs. Pin array shape displays are one example where this is particularly true. Many pin arrays use a row-column structure, as found on LCD screens, to reduce the number of inputs. However, reducing inputs in this manner makes simultaneous control of the pins challenging. Using semi-nonnegative matrix factorization (SNMF) to reduce the rank of the inputs solves this problem, but there has not yet been a method to analyze the stability of the resulting system. Additionally, the application of the SNMF System to pin arrays, particularly those using fluid power, presents many practical challenges. This paper proves that the SNMF rank-one approximation is strictly-output passive, leading to approaches to analyze the stability of the SNMF System. We also address practical challenges by showing that the SNMF System improves performance over the previous approach, line scanning, even in the presence of power limitations and by examining the effects of row and column dynamics and proposing approaches to limit these negative effects.