Laurentiu Hetel

Kun Liu, Emilia Fridman, Laurentiu Hetel

This paper develops the time-delay approach to Networked Control Systems (NCSs) in the presence of variable transmission delays, sampling intervals and communication constraints. The system sensor nodes are supposed to be distributed over a network. Due to communication constraints only one node output is transmitted through the communication channel at once. The scheduling of sensor information towards the controller is ruled by a weighted Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the existing results on NCSs in the presence of scheduling protocols (in the frameworks of hybrid and discrete-time systems), we allow the communication delays to be greater than the sampling intervals. A novel hybrid system model for the closed-loop system is presented that contains {\it time-varying delays in the continuous dynamics and in the reset conditions}. A new Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov functionals is introduced for the stability analysis of the delayed hybrid systems. Polytopic type uncertainties in the system model can be easily included in the analysis. The efficiency of the time-delay approach is illustrated on the examples of uncertain cart-pendulum and of batch reactor.

Mert Bastug, Laurentiu Hetel, Mihaly Petreczky

Two approaches to moment matching based model reduction of aperiodically sampled data systems are given. The term "aperiodic sampling" is used in the paper to indicate that the time between two consecutive sampling instants can take its value from a pre-specified finite set of allowed sampling intervals. Such systems can be represented by discrete-time linear switched (LS) state space (SS) models. One of the approaches investigated in the paper is to apply model reduction by moment matching on the linear time-invariant (LTI) plant model, then compare the responses of the LS SS models acquired from the original and reduced order LTI plants. The second approach is to apply a moment matching based model reduction method on the LS SS model acquired from the original LTI plant, and then compare the responses of the original and reduced LS SS models. It is proven that for both methods, as long as the original LTI plant is stable, the resulting reduced order LS SS model of the sampled data system is quadratically stable. The results from two approaches are compared with numerical examples.