Applications of Gröbner Bases to Nonlinear Systems

. Some problems within nonlinear control theory are stated and solved using so called Grobner bases from commutative algebra. The first problem is the one of stability and performance robustness of nonlinear systems subject to structured uncertainty. It is assumed that a Lyapunov function is given, and the quality of the solution depends on this Lyapunov function. It is also indicated how the robustness problem can be reinterpreted in different ways, e.g. in terms of controller design. The second problem is the one of finding a differential equation connecting the input and the output of a system starting from a state space description of it. In all cases the nonlinearities are required to be of polynomial type. The methods suggested are illustrated with concrete examples. Keywords: Nonlinear control systems, commutative algebra, Lyapunov theory, stability robustness, performance robustness, state space equations, input-output equation 1 Introduction. Lately there has been an increas..