Famous named curves generated as root loci produce optimum and pseudo-optimum stability designs for realistic systems. Non-minimum-phase control involves a principle of topological certainty. A root locus with complex breakpoints is discussed. Cassini's ovals in Brauer's method of eigenvalue localisation are illustrated. A problem in dielectric theory, recast into an imaginary-parameter root locus, is solved via real-parameter theory. Continuation, translation and scaling are invoked. It is hoped to impart an appreciation of the versatility of root-locus-inspired thinking.
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