This work continues our studies reported in the proceedings of the Optima conference in 2022 and 2023 [1, 2], where the problem of stabilizing a chain of three integrators by a piecewise continuous control in the form of nested saturators was discussed. In this work, we propose a AQ1 more advanced stabilizing control law. The new feedback control is con- tinuous and guarantees the fulfillment of a phase constraint imposed on the third state variable. We study global stability of the closed-loop sys- tem and set an optimization problem of determining feedback coefficients that ensure the greatest convergence rate near the equilibrium while pre- serving global asymptotic stability of the system. It is established that AQ2 the loss of global stability results from arising a hidden attractor, which comes to existence when the convergence rate reaches a critical value. A numerical procedure for constructing hidden attractors is developed, and the discussion is illustrated by numerical examples.