Abstract: The stability of bilinear systems is investigated using spectral techniques such as selective
modal analysis. Predictive models of bilinear systems based on inductive knowledge extracted by
big data mining techniques are applied with associative search of statistical patterns. A method and
an algorithm for the elementwise solution of the generalized matrix Lyapunov equation are developed
for discrete bilinear systems. The method is based on calculating the sequence of values of a
fixed element of the solution matrix, which depends on the product of the eigenvalues of the dynamics
matrix of the linear part and the elements of the nonlinearity matrixes. A sufficient condition
for the convergence of all sequences is obtained, which is also a BIBO (bounded input bounded
output) systems stability condition for the bilinear system.