We propose tools for the study of robust stabilizability and the design of robustly stabilizing feedback laws for a wide class of hybrid systems given in terms of hybrid inclusions with inputs and disturbances. We introduce notions of ro-bust uniform global stabilizability and stabilization that cap-ture the case when disturbances can be fully rejected, prac-tically rejected, and when they induce a residual set that can be stabilized. Robust control Lyapunov functions are em-ployed to determine when stabilizing static state-feedback laws are available and also to synthesize robustly stabiliz-ing feedback laws with minimum pointwise norm. Sufficient conditions on the data of the hybrid system as well as on the control Lyapunov function are proposed for the said proper-ties to hold. An example illustrates the results throughout the paper.

Given a dynamical system and a specification, assumption mining is the problem of identifying the set of admissible disturbance signals and initial states that generate trajecto-ries satisfying the specification. We first introduce the no-tion of a directed specification, which describes either upper or lower sets in a partially ordered signal space, and show that this notion encompasses an expressive temporal logic fragment. We next show that the order preserving nature of monotone dynamical systems makes them amenable to a systematic form of assumption mining that checks numerical simulations of system trajectories against directed specifica-tions. The assumption set is then located with a multidi-mensional bisection method that converges to the boundary from above and below. Typical objectives in vehicular traffic control, such as avoiding or clearing congestion, are directed specifications. In an application to a freeway ow model with monotone dynamics, we identify the set of vehicular demand profiles that satisfy a specification that congestion be intermittent.