A novel fractional order implicit dynamics method for solving time-varying linear matrix equation

In this paper, fractional order implicit dynamics (FOID) is first proposed and investigated for solving time-varying linear matrix equation $A(t) X(t) B(t)+X(t)=C(t)$ online. Unlike conventional neural-dynamic methods, the FOID introduces fractional calculus into neural dynamics. On the basis of the Lyapunov approach and linear frequency distributed model, a convergence theorem of the FOID model when $0\lt \alpha\lt2$ is put forward. Numerical simulation results further verify the validity and superiority of the FOID model in solving time-varying linear matrix equations regardless of initial value $X(0)$, compared with gradient neural network and Zhang neural network. In addition, the effects of fractional orders on convergence performance are also discussed.