Online Solution of Time-Varying Lyapunov Matrix Equation by Zhang Neural Networks

By constructing a matrix-valued unbounded error-function, this paper develops and exploits a new type of recurrent neural networks, named as Zhang neural networks, for the time-varying Lyapunov matrix equation with accuracy and effectiveness. In general, a scalar-valued norm-based energy function is defined for the design and development of the conventional gradient-based neural networks, which could only solve the time-invariant matrix equation exactly. Comparison with some recent patents on the neural networks designed originally for the time-invariant problems solving, the patents relevant to Zhang neural networks is designed for the solution of time-varying problems based on the matrix/ vector-valued error function. An illustrative example substantiates that the presented Zhang neural networks can effectively solve such matrix equation with time-varying coefficients, while the conventional gradient-based neural networks could only approximately approach to the theoretical solution.