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Two New Finite-time Convergence Criterions and Application to Solve Time Varying Sylvester Equation and Pseudo-inverse of a Matrix

Peng Miao*, Liujun Fan, and Daoyuan Zhang
International Journal of Control, Automation, and Systems, vol. 19, no. 4, pp.1570-1577, 2021

Abstract : Based on the second order differential equation, this paper investigates finite-time stability, finite-time convergence criterions and estimates of convergence time. The main contributions of this paper lie in the fact that two new finite-time convergence criterions are proposed through the property of the second order differential equation and their upper bound of the convergence time is derived. In addition, our finite-time stability criterions are used to a recurrent neural network for solving time-varying Sylvester equation and Pseudo-Inverse of a Matrix. At last, a numerical example and a Pseudo-Inverse of a Matrix demonstrate the effectiveness of our method.

Keyword : Convergence criterion, differential equation, finite-time stable, neural network, time-varying Sylvester equation, pseudo-inverse of a matrix.

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