On properties of gramians of continuous control systems

A new approach to the study of controllability and observabihty by means of analysis of the controhabihty and observabihty matrices and gramians was proposed. It rehes on the lemma of expansion of the matrix integrals proved by expanding the resolvents of the matrices A (m) and A and the properties of convolution of the matrix function in the complex domain. Analysis of the structural properties of gramians demonstrated that the coefficients of the characteristic equations and the Faddeev matrices in the decomposition of the resolvent of the system dynamics matrix play the leading part in their formation. An example illustrating the properties of gramians was given.