Abstract
We have presented mathematical connections among three stability criteria: (1) the Nyquist stability criterion for SISO systems; (2) the small gain theorem for unstructured perturbations in MIMO systems; and (3) the structured singular value for structured perturbations in MIMO systems. This connection can provide an intuitive understanding of MIMO stability analysis using singular values for those who have had prior exposure to the Nyquist stability criterion. Singular value techniques have been extended beyond the stability analysis presented here to performance analysis and robust control system design. This approach has been successfully used for many control problems, including a magnetically levitated train, helicopter control, aero-engine control, power conversion, active sound control, aircraft control, flexible space structure control and distillation process control. In the twentieth century, control theory evolved from classical control to modem control to optimal control to intelligent control. This evolution should continue and robust control (using the singular value techniques discussed here) will become more common in practice.
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