A note on observability tests for general polynomial and simple Wiener–Hammerstein systems

We propose an algorithm, based on symbolic computation packages, for testing observability conditions of general polynomial systems, which were formulated in Sontag, SIAM J. Control Optim. 17 (1979) 139–151. Computational complexity of the observability test can be reduced and the test simplified for classes of polynomial systems. We illustrate this by considering the class of simple Wiener–Hammerstein systems, which consist of a series of two linear dynamic blocks between which a static nonlinearity is “sandwiched”. We consider the case when the nonlinearity is a monomial . Simple necessary and sufficient conditions for observability are given and they resemble, but are subtly different from, the well known result on observability for the series connection of two linear systems.