Formal Power Series Approach to Nonlinear Systems with Static Output Feedback

The goal of this paper is to compute the generating series a closed-loop system when plant described in terms Chen-Fliess and static output feedback applied. first step reconsider so called Wiener-Fliess connection consisting followed by memoryless function. Of particular importance will be contractive nature map, which needed show that has representation. To explicitly series, two Hopf algebras are needed, existing algebra used describe dynamic feedback, shuffle group. These combinatorial structures combined what product. It shown product natural interpretation as transformation group acting on preserves relative degree plant.