Parametrization of the input-output image of nonlinear dynamic systems

For dynamic systems described by differential equations with smooth functions in the state space, the size of the parameter space is minimized such that the input-output image of the system is preserved by finding the complete set of algebraic invariants for a fixed structure of the equations of the system. A relationship between the constructs of the algebra of functions used in the problem and the mathematical constructs used in the differential geometric approach is established. A method for finding the algebraic invariants – the analogs of Markov parameters of linear systems – is described.