Detection of polynomial excitation

A mathematical analysis is worked out. Analytical conditions and equations are obtained. These are the basic requirements for drawing graphs to judge whether it is a question of polynomial excitation or not, and if so, to what degree. A simple procedure for the detection of polynomial excitation and its degree is developed. It is consists of continually changing, in a vast region, of the only time-invariant coefficient of a continuous second order system with polynomial varying coefficients. The enormous values of the measured output points out that the system is under polynomial excitation. If the values of the changeable coefficient, for which huge changes of the system output have occurred, is put on a graph and if a value of a natural number can be read out from the graph, than it surely is a question of polynomial excitation with a degree equal to the read out natural number