Wsbp function activated Zhang dynamic with finite-time convergence applied to Lyapunov equation

This paper investigates the solution of Lyapunov equation by neural dynamics. Specially, an improved finite-time Zhang dynamic (IFTZD), which is activated by weighted sign-bi-power (wsbp) function array, is proposed for Lyapunov equation solving. The proposed IFTZD model makes full use of all the items of the wsbp function, and thus obtains a more less conservative upper bound of the convergence time. Theoretical analysis shows that the IFTZD model has the best finite-time convergence as compared to existing neural dynamics. Moreover, an illustrative example is performed and the resultant results show that, for the proposed IFTZD model, the actual convergence time is less than but very close to the theoretical estimation of the upper bound of the convergence time. This has further demonstrated the theoretical analysis.