Sampled-data control with actuator saturated exponential synchronization semi-Markovian jump neural networks subject to input-to-state stability approach

• Published in: European physical journal plus Vol. 139; no. 8; p. 683
• Main Authors: Kumar, S. Santhosh, Chandrasekar, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 05.08.2024; Springer Nature B.V
• Subjects: Actuators; Applied and Technical Physics; Atomic; Closed loop systems; Closed loops; Complex Systems; Condensed Matter Physics; Control systems design; Controllers; Design; Dynamical systems; Feedback control; Hybrid systems; Mathematical and Computational Physics; Molecular; Neural networks; Nonlinear analysis; Nonlinear systems; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article; Stability; Systems analysis; Theoretical; Time synchronization; Time varying control
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-024-05470-y

In this study, we propose an advanced methodology for analyzing the exponential synchronization of semi-Markovian jump neural networks (SMJNNs) subjected to time-varying delay and controlled by a sampled-data controller. The analysis is based on a Wirtinger-based integral inequality (Li in Nonlinear Analysis Hybrid Systems 41:101028, 2021) and modified free matrix-based integral inequality (MFMBII) (Zeng in SN Applied Sciences 5:301, 2023), which provide a powerful framework for investigating complex dynamical systems. First, we establish a MFMBII, incorporating the dynamics of the SMJNNs and the time-varying delay. This inequality allows us to derive sufficient conditions for the exponential synchronization of the network systems. Then we proceed to derive two sufficient conditions that pertain to the design of the sampled-data controller. These conditions ensure the mean square input-to-state stability (ISS) for the hybrid closed-loop system. To achieve this, we employ the Lyapunov–Krasovskii functional (LKF) and the MFMBII approach. Lastly, the proposed input-to-state stabilization method is demonstrated numerically by using a numerical example that is used to verify its validity.