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Uncertainty of parameters in control systems was described by interval variables, and some idea of the non-probabilistic reliability method that we proposed in previous papers was used for stability analysis and synthesis of uncertain systems. A new method, called robust reliability method, was presented for quadratic stability analysis and robust stabilization of dynamic systems with interval parameters. In the method, the performance function for robust reliability calculation was established by criterion of quadratic stability, and a solving method in the form of optimization for robust reliability was presented. The proposed stabilization method can take both the required energy supply for control and the control robustness into account. This makes the reasonable strategy of compromising between the control cost and system reliability become possible. By the method, robust reliability measure of the stability degree of uncertain control systems can be provided, and the maximum allowable ranges of the basic parameters can be obtained. The presented method is based on the linear matrix inequality (LMI) approach, and is convenient to implement Three numerical examples were provided to illustrate the validity and efficiency of the presented method.