Abstract
In the algebraic approach to nonlinear control systems two similar notions, namely Kähler differentials and the formal vector space of differential one-forms having the properties of ordinary differentials, are frequently used to study the systems. This technical note explains that the formal vector space of differential one-forms is isomorphic to a quotient space (module) of Kähler differentials. These two modules coincide when they are modules over a ring of linear differential operators over the field of algebraic functions. Some remarks and examples demonstrating when the use of Kähler differentials might not be appropriate are included.
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