Abstract
The following problems are discussed and solved in this paper: finding computable necessary and sufficient conditions for complete reachability and complete observability of a linear, time-varying, discrete-time system; finding sufficient conditions for local controllability of nonlinear discrete-time systems; relating reachability to the concept of discrete Pfaffian systems; obtaining a minimal-dimension difference equation (with possibly variable coefficients) from a given input/output function of a system; finding necessary and sufficient conditions for Lyapunov stability and finite-time stability of nonlinear difference equations; and, giving an algorithm for determining whether a linear difference equation is stable in the finite-time sense.
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