A stability criterion for nonautonomous difference equations with application to the design of a digital FSK oscillator

We derive, by use of the Lyapunov theory for difference equations, a criterion for the asymptotic stability of a system governed by a nonautonomous difference equation of second order. The results are pertinent to the design of a simple digital frequency-shift-keying (FSK) oscillator. A feature of our analysis that is of major importance is the technique used in our application of the Lyapunov theory. It is shown that the technique yields the best stability criterion that can be obtained by the use of any positive definite quadratic form as a Lyapunov function. Thus we show how one might overcome one of the major obstacles to the practical application of the Lyapunov theory, i.e., the problem of choosing an appropriate (in some meaningful sense) Lyapunov function.