Methods and algorithms for obtaining analytical formulas for spectral decompo- sitions of gramians for bilinear multi-connected continuous stationary stable systems with a simple spectrum are developed. A guaranteed limited area of distribution of methods for solv- ing and analyzing linear control systems to a class of bilinear systems is found. New sufficient conditions for BIBO stability of bilinear systems are developed. The obtained spectral decom- positions of solutions by the spectrum of the dynamics matrix of the linear part, as well as the spectrum and residues of the images of actions, allow us to estimate their influence on the stability and dynamic characteristics of the bilinear system.