Effects of Time Delay Statistical Parameters on the Most Likely Regions of Stability in an NCS

In view of the fact that real networked control systems (NCSs) with uncertain events and traffic are subject to violation of the nominal conditions used in the design and analysis of their behavior, it is essential to consider (somehow) the probability of these conditions being (or not) fully satisfied. This paper focuses on practical issues and discusses the effect of the distributions of delays on the determination of the most likely stability regions to be considered in the design of a NCS. An alternative methodology for the analysis of NCSs is proposed here for implementation in real cases. The methodology is based on the Monte Carlo method coupled with a sorting algorithm and a gradient search using the analysis of time responses. The proposed method is compared with a traditional technique based on the polytopic overapproximation method to provide the maximum possible delays. The obtained results yielded less conservative stability limits, aligned with the tendency to use adaptive control techniques appropriate for practical NCS applications. Experimental results show that the upper bound of the delays that preserves the stability may be higher than the corresponding bound for the constant delay. Case studies presented in the paper show that the most likely region of stability of the considered NCSs is heavily dependent on the time-delays distributions. The obtained reduction of conservativeness warrants further investigation on method reliability in other cases.