Input-Output Gain Analysis of Linear Discrete-Time Systems With Cone Invariance

This article investigates the input-output gain of linear discrete-time cone-preserving systems. The cone linear absolute-norm and cone max-norm, which are applied to describe input-output gains of cone-preserving systems, are introduced. Subsequently, by utilizing the property of cone-preserving systems, several necessary and sufficient conditions to characterize input-output gains of the system in terms of cone-induced norms are provided. The results indicate that input-output gains of cone-preserving systems can be characterized by the static gain matrix. The duality between the two cone-induced gains is also unveiled.