Hamid Mcheick

Computer Science Department

University of Quebec at Chicoutimi

Chicoutimi, Quebec

Canada

**Author(s):**
Chen F. Yi and Yu H. Liu

**Affiliation: **Jiangxi University of Science and Technology, School of Information Engineering, No.86, Hongqi Ave., Ganzhou. Jiangxi.

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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**Article Details**

VOLUME: 6

ISSUE: 1

Page: [25 - 32]

Pages: 8

DOI: 10.2174/2213275911306010004