The convergence consensus of multi-agent systems controlled via doubly stochastic quadratic operators

This paper proposed doubly stochastic quadratic operators (DSQOs) for a consensus problem in multi-agent systems. The proposed scheme uses new nonlinear class model of family of quadratic stochastic operators (QSOs) for convergence consensus. The nonlinear model of QSOs plays an important role for reaching consensus. The nonlinear protocols for DSQOs are based on majorization theory. The paper investigates how the multi-agent systems converge to the optimal values (center) by using DSQOs. The proposed nonlinear model of DSQOs will be compared with the linear model of DeGroot and the nonlinear model of QSOs. Furthermore, we will show that the convergence of DSQOs is superior than DeGroot linear model and low-complex than QSOs nonlinear model.