  Flexible manufacturing has been the trend in the area of the modern chemical
process nowadays. One of the essential characteristics of flexible
manufacturing is to track time-varying target trajectories (e.g. diversity and
quantity of products). A possible tool to achieve time-varying targets is
contraction theory. However, the contraction theory was developed for
continuous time systems and there lacks analysis and synthesis tools for
discrete-time systems. This article develops a systematic approach to
discrete-time contraction analysis and control synthesis using Discrete-time
Control Contraction Metrics (DCCM) which can be implemented using Sum of Square
(SOS) programming. The proposed approach is demonstrated by illustrative
example.
