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This paper proposes and develops a generalized sector bound approach to feedback stabilization of nonlinear control systems described by state-space models. This approach is inherited from the methodology of the sector bounded or passive nonlinearities, and influenced by the concept of absolute stability. It aims not only to regionally stabilize the nonlinear dynamics asymptotically but also to maximize the estimated region of quadratic attraction and to ensure nominal performance at each equilibrium. Similar to gain scheduling control, a path of equilibria is programmed based on the assumption of centered-ϵ-cover which leads to a sequence of linear controllers that regionally stabilize the desired equilibrium asymptotically. Simulation results are worked out to illustrate our proposed design method.