Networked control systems induced delay modeling and stability analysis using Markov-regime-switching GARCH model

Abstract

This article focuses on the stability analysis of networked control systems (NCSs). It is well-known that network-induced delays pose many control challenges due to their non-uniform and multifractal nature. With the growing integration of communication networks in control systems, the impact of time-varying and random delays on system performance becomes critical. Hence, it is essential to study their impact on the system’s stability. There are several network-induced delay modeling methods, resulting in constant, random, and probabilistic random delays, which provide the most realistic representation according to recent studies. This article introduces a new network-induced delay modeling method based on the Markov-regime-switching generalized autoregressive conditional heteroskedasticity (MRS-GARCH) process, which captures the intricate temporal dependence of random network delays. The resulting model offers a more accurate depiction of delay volatility behavior, accommodating sudden shifts between volatility regimes. Simulation results demonstrate that MRS GARCH-type modeling enables a more realistic representation of delay dynamics. We also conduct a stability analysis of NCSs modeled with the proposed method using linear matrix inequalities LMIs criteria derived from the Lyapunov-Krasovskii theorem. The simulation results show less conservatism than conventional models and provide a larger maximum allowable upper delay bound MAUDB.