Fixed-Time Convergent Gradient Neural Network for Solving Online Sylvester Equation

This paper aims at finding a fixed-time solution to the Sylvester equation by using gradient neural network (GNN). To reach this goal, modified sign-bi-power (msbp) function is presented and applied on linear GNN as an activation function. Accordingly, convergent (FTC-GNN) model developed for solving equation. The upper bound of convergence time such FTC-GNN can be predetermined if parameters are given regardless initial conditions. point corroborated detailed theoretical analysis. In addition, also estimated utilizing Lyapunov stability theory. Two examples then simulated demonstrate validation analysis, well superior performance compared existing models.