In this paper we discuss the beginnings of an attempt to define and analyze the stability of an entire modular robotic system architecture -one which includes a three-tier (3T) layer breakdown of capabilities, with symbolic, deterministic planning at the highest level. We approach the problem from the standpoint of a control theory outlook, and try to formalize the issues that result from trying to quantitatively characterize the overall performance of a well-defined system without a need for exhaustive testing. We start by discussing the concept of bounded-input bounded-output stability, giving examples where the technique might not be sufficient to guarantee what we term "total system stability" due to complications associated with the levels of abstraction between the modules and components that are being chained together in the architecture. We then go on to discuss necessary conditions that may fall out of this naturally as a result. We further try to better-define the input and output constraints needed to guarantee total system stability, using an assumption-guarantee-like contractual framework that sits alongside the architecture; the requirements then may have influence across multiple modules, in order to keep consistency. We also discuss how the structure of the architectural modules may help or hinder the process of capability characterization and performance analysis of each module and a given architecture configuration as a whole. We then discuss two overlapping methods that, combined, should allow us to analyze the effectiveness of the architecture, and help towards verification and validation of both the components and the system as a whole. Demonstrative examples are given using a specific architectural implementation called the Resilient Spacecraft Executive. In future work, we hope to define both necessary and sufficient conditions for total system stability across such a system architecture for robotics use.