Monodromy and Isomonodromy for Linear $q$-Difference Systems with Coefficient Matrix $Ax+B$

In this paper, we construct canonical fundamental solutions for linear $q$-difference systems with coefficient matrix $Ax+B$, develop the associated isomonodromy theory, and study the differential limit as $q\to 1$. We determine the asymptotic behavior of generic isomonodromic deformations, and derive explicit formulas for their monodromy data in terms of their asymptotic leading terms. We also show that the differential limit as $q\to 1$ recovers the canonical fundamental solutions, the monodromy data, and the isomonodromic deformations of the corresponding differential systems.