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Complexity and large size of contemporary control, communication, and computer systems impose strong challenges to methods of their mathematical mod- elling, design, and testing. Classical approaches to their formal specication by ex- ploiting theory of systems on groups of real numbers R and complex numbers C, often do not fulll requirements of practice. For that reason, theory of systems on groups different from R and C has been developed. Differential operators and spectral (Fourier) analysis on groups play the same important role in such systems as in the case of systems modelled by signals dened on R and C. This paper rst briey reviews some aspects of research in system theory on groups and then presents an extension of the notion of Gibbs differentiation to matrix- valued functions on nite non-Abelian groups.

Remarks on systems and differential operators on groups