Finite-Time Stability Analysis for Resource Limited Chemical Reactions

We consider chemical reaction systems that operate in a resource limited situation such as in a closed test tube. These systems can operate only for a finite interval of time before the system variables deviate from the normal operating region. Thus, in order to characterize the performance of the systems, it is important to analyze the duration of the normal operation, which is closely related to the notion of finite-time stability. In this letter, we propose an algebraic optimization approach to analyze finite-time stability of resource limited chemical reactions. Specifically, we present semidefinite programs that compute guaranteed lower and upper bounds of the duration of the normal operation, which we call survival time, for a given set of uncertain initial concentrations. The proposed semidefinite programs provide progressively tighter bounds of survival time by increasing the variables and constraints, allowing for the tuning of the balance between the computational time and the conservativeness of the bounds. We demonstrate the proposed method using the regenerator circuit of DNA strand displacement reactions.