Controllability for a class of parallelly connected polynomial systems

Null controllability for a class of parallelly connected discrete-time polynomial systems is considered. We prove for this class of systems that a necessary and sufficient condition for null controllability of the parallel connection is that all its subsystems are null controllable. Consequently, the controllability test splits into a number of easy-to-check tests for the subsystems. The test for complete controllability is also presented and it is subtly different from the null controllability test. A similar statement is then given for complete controllability of a class of parallelly connected continuous-time polynomial systems. The result is somewhat unexpected when compared with the classical linear systems result. We identify the phenomenon which shows the difference between the linear and nonlinear cases.