| Summary: | Irrational Systems (ISs) are transfer functions that include terms with irrational exponents. Since such systems are ubiquitous and can be seen when solving partial differential equations, fractional-order differential equations, or non-linear differential equations; their nature seems to be strongly linked with a low-order description of distributed parameter systems. This makes ISs an appealing option for model-reduction applications and controls. In this work, we review some of the fundamental concepts behind a set of ISs that are of core importance in their stability analysis and control design. Specifically, we introduce the notion of multivalued functions, branch points, time response, and stability regions, as well as some practical applications where these systems can be encountered. The theory is accompanied by some numerical examples or simulations.
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