Model design and exponential state estimation for discrete-time delayed memristive spiking neural P systems

This paper investigates the exponential state estimation of the discrete-time memristive spiking neural P system (MSNPS). The spiking neural P system (SNPS) offers algorithmic support for neural morphology computation and AI chips, boasting advantages such as high performance and efficiency. As a new type of information device, memristors have efficient computing characteristics that integrate memory and computation, and can serve as synapses in SNPS. Therefore, to leverage the combined benefits of SNPS and memristors, this study introduces an innovative MSNPS circuit design, where memristors substitute resistors in the SNPS framework. Meanwhile, MSNPS mathematical model is constructed based on circuit model. In order to be more practical, the time delays in the system are analyzed in addition to the discretization of the continuous MSNPS. Moreover, some sufficient conditions for exponential state estimation are established by utilizing a Lyapunov functional to MSNPS. Finally, a numerical simulation example is constructed to validate the main findings.