Input-To-State Stable Sampled-Data Synchronisation Of Markovian Jump Lur’e Networks Under Actuator Saturation

This paper tackles the challenge of achieving Input-to-state stable (ISS) synchronization in actuator-saturated sampled-data control (SDC) networks for Markovian jump (MJ) Lur’e networks. We investigate the impacts of actuator saturation on system performance and stability, proposing a control strategy that ensures synchronization in the presence of external disturbances. Our analysis employs a Wirtinger-based integral inequality alongside a modified free matrix-based integral inequality (MFMBII), providing a framework for examining Lur’e networks. Initially, we create an MFMBII that combines the dynamics of MJ Lur’e networks and takes into consideration time-varying delays. Second, we formulate two sufficient conditions for the SDC design that ensure mean-square ISS error of specification for the hybrid closed-loop system. We do this by combining the MFMBII method with the Lyapunov-Krasovskii functional (LKF). Through a systematic methodology, we demonstrate that the proposed method maintains bounded state responses and converges to a common trajectory at an exponential rate. The results highlight the effectiveness of integrating ISS with SDC in managing complex dynamical networks. Finally, the proposed ISS method is validated through a numerical example, confirming its efficacy.