О РЕШЕНИИ ОБОБЩЕННЫХ УРАВНЕНИЙ ЛЯПУНОВА ДЛЯ ОДНОГО КЛАССА НЕПРЕРЫВНЫХ БИЛИНЕЙНЫХ НЕСТАЦИОНАРНЫХ СИСТЕМ

The problem on solving both homogeneous and non homogeneous generalized linear vector equations in idempotent algebra is considered. In order to examine the equations, an idempotent analogue of matrix determinant is introduced, and its properties are investigated. The general solutions of the equations are obtained, and related existence conditions are established provided that the matrix is irreducible. The results are then extended to cover the case of arbitrary matrix. As a consequence, the solution of homogeneous and non homogeneous inequalities is also presented.