Remote Stabilization of Networked Control Systems with Unknown Time Varying Delays by LMI Techniques

In this paper, the stabilization of one class of remote contorl systems with unknown time varying delays is analyzed and discussed using LMI techniques. A discrete time state space model under a static control law for remote control systems is first introduced based on some assumptions on the uncertain term. The time delay is unknown time varying, and can be decomposed into two parts: one fixed part which is unknown and is an integer multiple of the sampling time; the other part which is randomly varying but bounded by one sampling time. Static controller designs based on delay dependent stability conditions are presented. This system is then extended to a more general case when the randomly varying part of the time delay is not limited to one sampling time. The derivative of the time delay is not limited to be bounded. Hence, the contributions are as follows: i) for a given controller, we can use these stability criteria to test stability of the resulted system; ii) we can design a remote controller to stabilize an unstable system. Finally, a simulation example is presented to demonstrate the remote stabilization of open loop unstable systems.