Secondary safety control for systems with sector bounded nonlinearities

We consider the problem of safety verification and safety-aware controller synthesis for systems with sector bounded nonlinearities. We aim to keep the states of the system within a given safe set under potential actuator and sensor attacks. Specifically, we adopt the setup that a controller has already been designed to stabilize the plant. Using invariant sets and barrier certificate theory, we first give sufficient conditions to verify the safety of the closed-loop system under attacks. Furthermore, by using a subset of sensors that are assumed to be free of attacks, we provide a synthesis method for a secondary controller that enhances the safety of the system. The sufficient conditions to verify safety are derived using Lyapunov-based tools and the S-procedure. Using the projection lemma, the conditions are then formulated as linear matrix inequality (LMI) problems which can be solved efficiently. Lastly, our theoretical results are illustrated through numerical simulations.