The quantum mechanical entropy of density matrices defined by Von Neumann in quantum physics has been generalized in the form of quantum entropy of non-probabilistic matrices, and it is shown that the latter can be of some use in automatic control. This quantum entropy can be thought of as a measure of structure complexity and its application is quite relevant and meaningful in the following topics: stability of linear and non-linear systems, robustness and order reduction. Quantum entropy appears to be a new weighted combination of eigenvalues which would allow us to re-examine some problems with new points of view relating to information theory without probability.