Output Feedback Synchronization for Delayed Neural Networks Based on a Semi-Markov Approach

To address the problem of static output feedback master-slave synchronization in semi Markov neural networks with time-varying delays, a static output feedback controller was designed to achieve synchronization between the semi Markov neural network slave system and the master system under the influence of time-varying delays. A semi-Markov switching process was used to model time-varying time-delay neural network systems, and to characterize the phenomenon of sudden changes in neural network system parameters. Compared to Markov processes, semi Markov processes were more general. Considering the situation where the system state couldn’t be fully obtained, the output information was used to achieve synchronization between neural networks. Using Lyapunov stability theory, selecting time-delay dependent Lyapunov functionals and combining them with integral inequality scaling techniques to obtain sufficient conditions for low conservatism. In the absence of a controller input matrix, the free weight matrix technique was used to separate the system matrix from the Lyapunov functional generalized matrix, overcoming the conservatism of a fixed weight matrix. Finally, the effectiveness of the controller design was verified through one numerical example. The results show that the designed controller can still eliminate errors and achieve synchronization in 5 s even when the initial state of the time-varying time-delay system is not synchronized with the main system. The control signal also tends to stabilize after eliminating errors, ensuring the random mean square stability of the synchronization error system while meeting the mixed infinite/passive performance indicators, proving the rationality of the design.