INVERTIBILITY OF CAUSAL DISCRETE-TIME DYNAMIC-SYSTEMS

We show that a causal discrete time dynamical system, which is represe nted by a difference equation, can be written as x(t) = F(x(t - 1)), w here the Jacobian matrix partial derivative F/partial derivative x is non-singular. This invertibility or reversibility property, which is t he analogue of the one-parameter group associated with a dynamical sys tem represented by an ordinary differential equation, is obtained via techniques resulting from difference algebra.