To extend this verification approach to handle nonlinear systems, one could employ techniques such as Taylor model-based reachability analysis or interval arithmetic to approximate the dynamics of the system. By using these methods, the nonlinear system can be over-approximated by a set of linear systems, allowing for the application of the existing linear verification techniques. For hybrid systems, one could incorporate techniques from hybrid systems verification, such as reachability analysis for hybrid systems or abstraction techniques that capture both continuous and discrete dynamics. By combining these approaches, the verification of nonlinear and hybrid systems against temporal logic specifications can be achieved.