FUNCTIONAL DIFFERENTIAL EQUATIONS OF LOSSLESS PROPAGATION AND ALMOST LINEAR BEHAVIOR

Starting from various models in control and electrical engineering, there is obtained a rather general model of an IBVP(Initial Boundary Value Problem) for hyperbolic PDE(Partial Differential Equations) with the boundary conditions connected in feedback to some systems described by ODE(Ordinary Differential Equations - lumped parameter systems). To this model it is associated a special class of FDE(Functional Differential Equations) - delay equations coupled to continuous time difference equations. This survey examines stability and oscillation problems for such systems within the framework underlined by the dialectics Liapunov function/Popov frequency domain inequalities. Several open problems are equally mentioned.