Stability of networked control systems with variable sampling and delay

We consider Networked Control Systems (NCSs) consisting of a LTI plant; a linear static or dynamic feedback controller; a collection of sensors that provide measurements to the controller; and a collection of actuators that are used to control the plant. The different elements of the control system are spatially distributed, but interconnected through a communication network. Due to the shared and unreliable channel used to connect the subsystems, the sampling intervals are uncertain and variable. Moreover, samples may be dropped and experience uncertain and variable delays before arriving at the destination. We show that the resulting NCSs can be viewed as a MIMO sampled-data system with variable sampling intervals and delay, which can be modeled by linear infinitedimensional impulsive systems. The infinite dimensionality of the system arises from the existence of delays. We provide conditions for the stability of the closed-loop expressed in terms of LMIs. By solving these LMIs, one can determine positive constants related to each entity sent through the network that determines an upper bound between the sampling time and the next update time at the destination of that entity, for which stability of the closed-loop system is guaranteed.