What are the challenges in multivariable (MIMO) control system design?

MIMO systems have interactions between control loops - one input affects multiple outputs. Challenges include: interaction analysis (Relative Gain Array quantifies coupling), loop pairing (match inputs to outputs), decoupling (design compensators to minimize interaction), directionality (different gains in different input/output directions - singular value decomposition), and right-half-plane zeros (limit achievable bandwidth in specific directions). Classical SISO methods fail; use frequency-domain methods (SVD, Nyquist) or state-space (LQR, pole placement). Coordinated controller design is essential.