Control of asynchronous dynamical systems with rate constraints on events

We consider dynamical systems which are driven by external “events” that occur asynchronously. It is assumed that the event rates are fixed, or at least they can be bounded on any time period of length T. Such systems are becoming increasingly important in control due to the very rapid advances in digital systems, communication systems, and data networks. Examples of asynchronous systems include, control systems in which signals are transmitted over an asynchronous network, parallelized numerical algorithms, and queuing networks. We present a Lyapunov-based theory for asynchronous dynamical systems and show how Lyapunov functions and controllers can be constructed for such systems by solving linear matrix inequality (LMI) and bilinear matrix inequality (BMI) problems. Examples are also presented that demonstrate the effectiveness of the approach in analyzing practical systems