A recurrent neural network for solving Sylvester equation with time-varying coefficients

Authors:
Yunong Zhang;Danchi Jiang;Jun Wang
Affiliations:
Dept. of Autom. & Comput.-Aided Eng., Chinese Univ. of Hong Kong, Shatin;-;-
Venue:
IEEE Transactions on Neural Networks
Year:
2002

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Abstract

Presents a recurrent neural network for solving the Sylvester equation with time-varying coefficient matrices. The recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time-varying solution of a given Sylvester equation. Theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network. Simulation results of time-varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network.