Stability of networked control systems with asynchronous renewal links: An impulsive systems approach

We consider networked control systems in which sensors, actuators, and controller transmit through asynchronous communication links, each introducing independent and identically distributed intervals between transmissions. We model these scenarios through impulsive systems with several reset maps triggered by independent renewal processes, i.e., the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals. For linear dynamic and reset maps, we establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one. We also prove that the origin of a non-linear impulsive system is (locally) stable with probability one if its local linearization about the zero equilibrium is mean exponentially stable, which justifies the importance of studying the linear case. The applicability of the results is illustrated through an example using a linearized model of a batch-reactor. Keywords : Networked control systems; Stability of stochastic systems; Asynchronous systems; Impulsive systems; Positive systems