How do you analyze a multivariable (MIMO) control system for interaction and controllability?

Analysis methods: RGA (Relative Gain Array) - indicates pairing and interaction severity (diagonal elements near 1 indicates good pairing, negative elements indicate unstable pairing); SVD (Singular Value Decomposition) - determines controllability and directionality (condition number indicates sensitivity); Niederlinski Index - stability requirement for integral control; CLDG (Closed Loop Disturbance Gain) - disturbance rejection analysis. Process: develop linear model (G matrix), calculate RGA, determine variable pairing, assess interaction severity, decide between decentralized PID vs MPC, and design accordingly.