Issues of the asymptotic stability for linear difference equations with time-varying coefficients are discussed. It is shown that, in contrast to equations with constant coefficients, the condition of Schur stability of the characteristic polynomial for a linear difference equation with time-varying coefficients is neither necessary nor sufficient for the asymptotic stability of the difference equation. It is proved that the analog of Kharitonov's theorem on robust stability and the edge theorem do not hold for a difference equation if the coefficients of the equation are not constant.

We consider a bilinear control system defined by a linear time-invariant system of differential equations with multiple lumped and distributed delays in the state variable. A problem of finite spectrum assignment is studied. One needs to construct control vectors such that the characteristic function of the closed-loop system is equal to a polynomial with arbitrary given coefficients. We obtain conditions on coefficients of the system under which the criterion was found for solvability of this finite spectrum assignment problem. This criterion is expressed in terms of rank conditions for matrices of the special form. Corollaries on stabilization of a bilinear system with delays are obtained. An illustrative example is presented.