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Reliable biochemical implementations of linear controllers can provide a large set of tools for the design and analysis of control in Synthetic Biology. Theoretical frameworks are now available to represent feedback control systems as chemical reaction networks which can be readily translated into equivalent nucleic acid-based chemistry. However, the development of tools for constructing and analysing such controllers is still in its infancy. Nucleic acid-based chemistry is a strong candidate framework for the construction of future synthetic biomolecular control circuits. The capacity of strand displacement reactions with Deoxyribonucleic Acid (DNA) to implement analogue signal processing in vitro and in vivo makes them a promising candidate to embed synthetic feedback control circuitry in biomolecular environments. However, little progress has so far been made in developing the requisite theoretical machinery to inform the systematic design of feedback controllers in this context. Here, the potential complexity of such controllers is extended significantly by showing how time-delays, numerical differentiation (to allow proportional-integral-derivative control), and state feedback may be implemented via chemical reaction network-based designs. This work also provides a number of foundational theoretical results on the equilibria, stability, and dynamics of nucleic acid controllers, and the analysis highlights the many interesting and unique characteristics of this important new class of feedback control systems. In particular, that the implementation of feedback controllers using DNA strand displacement reactions introduces additional nonlinear dynamics, even in the case of purely linear control designs, and a robust design of the linear system does not imply the robustness of its chemical implementation. The robustness of the controllers to experimental uncertainty is analysed with the structured singular value (µ) analysis tool, which is extended with a model of how parametric uncertainty in the system affects the location of its equilibrium. This framework provides more reliable results than sampled based statistical methods, where analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by µ-analysis. The implementations of the examples and controllers in nucleic acid-based chemistry are simulated and checked using the Visual DSD simulation package, a bespoke software tool for simulating nucleic acid-based circuits.