  Switching controllers play a pivotal role in directing hybrid systems (HSs)
towards the desired objective, embodying a ``correct-by-construction'' approach
to HS design. Identifying these objectives is thus crucial for the synthesis of
effective switching controllers. While most of existing works focus on safety
and liveness, few of them consider timing constraints. In this paper, we delves
into the synthesis of switching controllers for HSs that meet system objectives
given by a fragment of STL, which essentially corresponds to a reach-avoid
problem with timing constraints. Our approach involves iteratively computing
the state sets that can be driven to satisfy the reach-avoid specification with
timing constraints. This technique supports to create switching controllers for
both constant and non-constant HSs. We validate our method's soundness, and
confirm its relative completeness for a certain subclass of HSs. Experiment
results affirms the efficacy of our approach.
