Summary: The general quadratic \(L_2\) gain analysis of uncertain jump systems plays an important role to its stabilization and robustness. We present a robust control law with mode-dependent state feedback such that the resulting jump system satisfies given input-and-output \(L_2\) gain constraints. There are two components of uncertainty. First, the uncertainty of transition rate among different modes is bounded by a convex polytope. Second, the time-varying uncertain parameters of state equation are characterized by a selected \(L_2\) gain. In a probability space, the obtained feedback control law is robust against uncertainties of transition rate and time-varying parameters. Using linear matrix inequality technique and convex optimization computing, we can readily implement the synthesis of feedback control law. Finally, a computing example is given.