Generalisation of D decomposition techniques

The technique of D decomposition has been generalised to provide what is believed to be the most powerful method presently available for the study, particularly the synthesis, of asymptotically stable, linearised, multiparameter autonomous systems. In particular, the method has been developed so that only one (any one) parameter need be restricted to appearing linearly in the characteristic equation. The other parameters may enter in any way whatsoever, so that it is virtually impossible to conceive of a practical system which does not fall within the scope of the method. Further, the method has been generalised so that not only the zero-damping case can be synthetised, but also the cases of arbitrarily specified degrees of absolute or relative stability. The method has been designed for use with a digital computer, and all essential algorithms required in its application are outlined. Special attention has been given to the general possibilities for the partitioning of an arbitrary characteristic equation, and as a result it has been found possible to develop procedures which permit the determination, in advance of any computation of the most efficient partitioning and parameter selection for any given problem. Comparisons are made with the Routh-Hurwitz method, and these show the Ddecomposition technique to be much the superior. Data has been published earlier showing the superiority of this method compared with root-locus methods.