In this paper, the mathematical expressions of a second-order matrix sensitivity analysis (SOMSA) is derived. This method has higher accuracy and requires less calculation works than previous analysis methods. Based on the SOMSA, when the traditional force-based impedance control is applied in leg hydraulic drive system (LHDS) of legged robots, the effects of parameter variations on control performance are studied by sensitivity dynamic analysis under nine working conditions. Then, combined with two measurable sensitivity indexes, the results of the sensitivity dynamic analysis are studied quantitatively. Finally, the above results are verified experimentally by using LHDS test platform. The conclusions contribute to the optimization of the LHDS structure and provide theoretical references for compensation control strategies of the traditional force-based impedance control. •New sensitivity analysis method called second-order matrix sensitivity analysis(SOMSA) is proposed.•Effects of parameter variations on control performance of force-based impedance control is studied.•Sensitivity dynamic analysis is conducted for twelve main parameters under nine working conditions.•Sensitivity dynamic analysis are studied quantitatively by combining with two measurable sensitivity indexes.