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Introductory state-space linear control courses focus on linear,time-invariant systems and spend intense efforts by introducing systemrealizations that allow the student to grasp fundamental concepts, among whichcontrollability, observability, and controller and observer design. This notedescribes a graphical mechanism to transform a system expressed inobservability form into its observer form based on elementary block diagrammanipulations, a technique whose pedagogical usefulness tends to be overlooked.Given the well-known duality principle in linear systems with respect tocontrollability and observability, the proposed graphical mechanism isapplicable to transform from controllability to controller realization.

From Observability to Observer Realization: A path via elementary block-diagram manipulations