Simultaneous stabilization of multiple equilibrium points

With reference to a class of nonlinear systems exhibiting more unstable equilibrium points, possibly in conjunction with stable ones, the paper presents a state-feedback control strategy capable of simultaneously stabilizing them all. The proposed control law, which does not require explicit knowledge of the equilibria, entails evaluating the Jacobian of the original transition function at the current state and contains a matrix parameter that can be adjusted to modify the domains of attraction and to moderate the control efforts. The effectiveness of the procedure is illustrated with the aid of meaningful examples.