Stability of Asynchronous Networked Linear Control Systems with Direct-Feedthrough Terms and Scheduling Protocols

In this paper, we analyze the stability of a linear control system where the plant and controller, both containing direct-feedthrough terms, communicate asynchronously over a network using scheduling protocols. The overall system is modeled as a hybrid dynamical system and sufficient conditions for its closed-loop stability are derived using a new Lyapunov function. Additionally, we define a stability property that is associated with the feedthrough terms and the adopted scheduling protocols and, subsequently, derive verifiable conditions that evaluate the aforementioned stability property. The effectiveness of the results is demonstrated through numerical simulations on a benchmark model, and effects of user-specified parameters are examined.