System-level Properties as Numerical Invariants

This chapter summarizes an attempt to express classical notions of control theory such as stability or robustness using the previously presented invariant-based tools. All numerical tools presented in previous chapters were focused on the precise over-approximation of reachable states. However, this chapter argues that it is important to be able to express higher level properties than just bounding reachable states. The idea that drove the invariants and template synthesis after all was this notion of Lyapunov functions and of Lyapunov stability. Assuming a control level property, it would be extremely interesting to be able to express this property over the code or model artifact. A main limitation for the study of these control level properties is the need for the plant description, which is generally not available when considering code artifact. As such, this chapter assumes the plant semantics is provided in a discrete fashion and therefore amenable to code level description as presented in Chapter 3.