ABSTRACT. We study the problem of computing input signals that produce system behaviors that falsify requirements written in temporal logic. We provide a method to automatically search for falsifying time varying uncertain inputs for nonlinear and possibly hybrid systems. The input to the system is parametrized using piecewise constant signals with varying switch times. By applying small perturbations to the system input in space and time, and by using gradient descent approach, we try to converge to the worst local system behavior. The experimental results on non-trivial benchmarks demonstrate that this local search can significantly improve the rate of finding falsifying counterexamples.