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Root Locus Design Calculate and plots the root locus of a SISO system. Controllability and Observability Construct the controllability and observability matrices. Determines the controllability and observability of systems. Calculates the controllability and observability grammians of a state-space model. State-Space Design Oct 22, 1993 · Root locus plots are calculated by solving a complex valued polynomial equation -- but it isn't really necessary to do the math. The beauty of the root locus method is that RL plots can be sketched by following a set of simple rules that require only a little algebra. Root Locus Plotting Rules. See handout Rework the example using the rules.