Dyadic Expansions and Multi-variable Feedback Design

The lecture will review and motivate the use of dyadic expansions in the analysis and design of unity negative feedback control configurations for the control of linear, time invariant systems denoted by an mxm transfer function matrix G (s). The approach is formulated as a systematic attempt to reduce the structural complexity of the design problem by "equivalence transformation of G (s)" and hence, to replace the problem by one of greater simplicity. The potential of the transformation technique is illustrated by application to the class of system described by "dyadic transfer function matrices". Finally the ideas are combined with the important concept of "diagonal dominance" to generate a "general dyadic decomposition" suitable for the systematic manipulation " compensation of system characteristic loci". Some relationships with the concepts of "multi-variable root-loci" are also outlined.