Robust Multiplicative Control in Chemical Reaction Networks Extended Version

Achieving complex multi-species control objectives is essential for engineering advanced autoregulated biomolecular devices. This paper addresses the problem of robust steady-state tracking for outputs defined as multiplicative combinations of biomolecular species concentrations. We first introduce a control architecture realized via chemical reaction networks that steers the product of two target species concentrations in the controlled network to a prescribed value. A robust stability analysis is provided for closed-loop system families with distinct structural characteristics. The proposed framework is also extended to a more general formulation capable of regulating arbitrary monomial outputs involving multiple species. Numerical simulations of representative examples corroborate the theoretical results and illustrate the effectiveness of our approach.