Stability of high order polynomial dynamics and minimum phase discrete-time systems

The definition of a minimum phase nonlinear system, as usually found in the literature, is not general enough to be used for some classes of systems. The nonlinearity may yield a variety of different behaviors that are not addressed and analyzed in the literature. We provide a constructive method to test several different minimum phase properties for classes of explicit and implicit discrete-time polynomial systems. The method is based on a symbolic computation package called QEPCAD. Our results can also be interpreted as a constructive approach to stability and stabilizability of explicit and implicit discrete-time polynomial systems.