New Criteria of Event-triggered Exponential State Estimation for Delayed semi-Markovian Memristor-based Neural Networks

This paper focuses on the exponential state estimation issue for Memristor-based Neural Networks (MNNs) with semi-Markov Jump Parameters (semi-MJPs) and Time-varying Delay (TD). At first, an alternative way obtains a tighter bound of the Exponential-type Integral Quadratic Terms (EIQTs) is introduced by establishing a novel Exponential-type Free-matrix Integral Inequality (EFMII), which contains some existing integral inequalities as its special cases. Next, a Sampled-data-based Event-triggered Control Mechanism (SECM) is introduced to further save the limited network resources. Moreover, a proper Lyapunov-Krasovskii Functional (LKF) is structured by getting the utmost out of the information of decay exponent, semi-MJPs, and TD. Then, by using the EFMII and SECM, three new kinds of less conservative criteria ensuring the exponential stability of the underlying error systems are found in terms of Linear Matrix Inequalities (LMIs), and the corresponding state estimators are well designed. At last, the validity of the proposed theoretical results is shown by three numerical simulation examples.

Automated summary

This paper addresses the issue of exponential state estimation for Memristor-based Neural Networks (MNNs) with semi-Markov Jump Parameters (semi-MJPs) and Time-varying Delay (TD). It introduces an alternative method to obtain tighter bounds for Exponential-type Integral Quadratic Terms (EIQTs) by establishing a novel Exponential-type Free-matrix Integral Inequality (EFMII). A Sampled-data-based Event-triggered Control Mechanism (SECM) is proposed to save network resources, and a proper Lyapunov-Krasovskii Functional (LKF) is structured to leverage the information of decay exponent, semi-MJPs, and TD. Less conservative criteria for exponential stability are found and state estimators are designed using the EFMII and SECM. Numerical simulation examples are provided to validate the proposed theoretical results.