Uniform observability conditions for a class of polynomial systems

The problem of obtaining the estimate of universal polynomial inputs degree from Sussman's theorem about the universal inputs for polynomial systems is considered. The estimate depends on the relative degree of the ″system-observation law″ pair and system dimensionality and characterizes the structure of a set of the universal polynomial inputs in the space of polynomial inputs. Some examples are presented. The relation of the obtained estimates to properties of uniform observability is discussed.