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.
Keywords: Energy function, error function, gradient algorithm, time-varying matrix equation, recurrent neural networks.
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