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This brief presents a systematic approach for the design of a robust decoupling precompensator using an approximate right inverse (ARI) of a system, where the problem of finding an ARI is presented as an L2-gain minimization problem. Furthermore, new LMIs are presented to analyze worstcase L2-gain for an uncertain system. These LMIs use extra variables to eliminate product terms between system state matrices and the Lyapunov matrix. This elimination enables the use of a parameter dependent Lyapunov function in a systematic way. These LMIs are extended to synthesis both constant and dynamic precompensators as well. Using the synthesis and the analysis LMIs, a combined genetic-LMI-algorithm is also presented to find a suitable precompensator that achieves diagonal dominance for systems with input uncertainties. Some previously presented LMIs for pole clustering are also modified to make them compatible with newly presented LMIs. The proposed approach is applied to the design of a high integrity robust multiinput multioutput controller for a process control rig which consists of a temperature and a flow rate control loop. The system has an input uncertainty of about 20%. It is shown that the closed-loop system poses a high integrity while being robust with respect to input uncertainties. The controller is also applied to the real plant to verify that the proposed algorithm and the desired results are obtained.