Stabilization of Markov Jump Systems With Delay by Discrete-Time Aperiodically Intermittent Stochastic Control Based on Lévy Noise
Xin Liu, Pei Cheng, Feiqi Deng, Ting Cai · IEEE Transactions on Circuits and Systems I Regular Papers · 2025
This paper investigates how to stabilize unstable Markov jump systems with delay (MJSs-D) using non-Gaussian white noise based on sampled observations. First, the study addresses the noise stabilization problem of the corresponding delay-free Markov jump systems (MJSs). Using the Lyapunov function method and the stationary distribution of Markov chains, an aperiodic intermittent stochastic control based on Lévy noise (AISC-LN) is developed. The analysis of the low-order moment exponential stability of stochastic controlled systems is comprehensively based on the ergodicity of the Markov chain, making the derived criterion less restrictive than the traditional one underM-matrix-based conditions. Subsequently, leveraging the auxiliary system method and comparison principle, the AISC-LN based on discrete-time state and mode observations is proposed for MJSs-D. This strategy encompasses specific cases such as discrete-time feedback control and periodic intermittent control based on Brownian motion, furthermore highlights the stabilizing effects of Markov chains and Poisson white noise, thereby providing a definitive answer to the proposed problem. The new control scheme applies to MJSs-D with various types of relatively small delays. Finally, the feasibility and accuracy of the conclusions are validated through an example of a DC-DC buck converter circuit.