A new FXTZNN model for solving TVCS equation and application to pseudo-inverse of a matrix

In order to obtain a smaller upper bound of convergence time (UBCT), a new fixed-time stability (FXTS) criterion is given. On this basis, a fixed-time zeroing neural network (ZNN) model is designed to solve time-varying complex Sylvester (TVCS) equation and the method is used to find pseudo-inverse of a matrix. A new positive definite and radially unbounded function with an exponential term is designed to achieve FXTS of the nonlinear dynamical system. To do so, the UBCT is obtained by taking logarithms, so that it is smaller than others under the same conditions. While, the proposed FXTS criterion is proven and the UBCT independent of initial point is estimated. Then, a fixed-time ZNN (FXTZNN) model is designed to solve TVCS equation and its FXTS is proven. In addition, a noise interference term is added into the proposed ZNN model, its noise-tolerant is analyzed and the steady-state error is given. Lastly, two numerical illustrative examples and an application example show the superiority and effectiveness of our methods.