Proportional–Integral State Estimator for Quaternion-Valued Neural Networks With Time-Varying Delays

Stability analysis of systems with time‐varying delay via a delay‐product‐type integral inequality

“…Inspired by PID theory, integral, proportional, and derivative denote the information about past, present, and future, respectively, a set of time series about the integral of the state vector, the state vector, and the derivative of the state vector are utilized in the quadratic term of the augmented LKF. In some existing literature, 21–23 only the derivative of the state vector and the state vector are considered in the quadratic term of the LKF; if more integral terms of the state vector are considered, then more information about the instant vector and the delayed state vectors can be utilized. Hence, by adding the integral terms to χ ( t ), an augmented LKF is tailored for the use of the DPT integral inequality; then, the integral terms can be closely coupled by P , that is, the relationship between the integral terms on the LKF derivative can be enhanced by the coupling.…”

“…The advantage of the augmented LKF is that more information about the instant state and the delayed states is taken into account compared with the LKFs in previous studies. [21][22][23] As a result, much better performance can be obtained. Remark 4.…”

Model‐free adaptive tracking control for networked nonlinear systems with data dropout

“…For instance, if there is data dropout at time instant k, controller cannot receive the output data y(k) successfully, which will degrade the tracking performance. It is known that neural network [42][43][44] is often used for system modeling. Due to the simple network structure and powerful approximation ability, 45,46 a RBFNN compensation algorithm is given to diminish the adverse impact of data dropout.…”

Synchronization of Generally Uncertain Markovian Inertial Neural Networks With Random Connection Weight Strengths and Image Encryption Application

“…I N recent years, neural networks have received considerable attention because of their broad applications in pattern recognition, associative memories, signal processing and secure communication, etc [1]- [8]. Due to the finite switching speed of the amplifier, time delays often occur between neurons and may result in complicated chaotic dynamics [3]- [12].…”