This paper presents a systematic approach to exponentially stabilize periodic orbits in nonlinear systems with impulse effects, a special class of hybrid systems. Stabilization is achieved with a time invariant continuous-time controller. The presented method assumes a parametrized family of continuous-time controllers has been designed so that (1) a periodic orbit is induced, and (2) the orbit itself is invariant under the choice of parameters in the controllers. By investigating the

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... of the Poincaré return map, a sensitivity analysis is presented that translates the stabilization problem into a set of Bilinear Matrix Inequalities (BMIs). A BMI optimization problem is set up to select the parameters of the continuoustime controller to achieve exponential stability. We illustrate the power of the approach by finding new stabilizing solutions for periodic orbits of an underactuated 3D bipedal robot.