  This paper explores the design of hybrid feedback for a class of affine
nonlinear systems with topological constraints that prevent global asymptotic
stability. A new hybrid control strategy is introduced, which differs
conceptually from the commonly used synergistic hybrid approaches. The key idea
involves the construction of a generalized synergistic Lyapunov function whose
switching variable can either remain constant or dynamically change between
jumps. Based on this new hybrid mechanism, a generalized synergistic hybrid
feedback control scheme, endowed with global asymptotic stability guarantees,
is proposed. This hybrid control scheme is then improved through a smoothing
mechanism that eliminates discontinuities in the feedback term. Moreover, the
smooth hybrid feedback is further extended to a larger class of systems through
the integrator backstepping approach. The proposed hybrid feedback schemes are
applied to solve the global obstacle avoidance problem using a new concept of
synergistic navigation functions. Finally, numerical simulation results are
presented to illustrate the performance of the proposed hybrid controllers.
