The authors investigate the robust gamma stability problem of linear time invariant systems with state space representations. The perturbations of concern are assumed to be time invariant with some given structures. Based on real stability radii, they derive various stability robustness criteria such that all the eigenvalues of the perturbed systems are kept in a specified region, a wedge or a disc in the complex plane. Both the cases of continuous-time and discrete-time systems are discussed. The authors also propose a convergent algorithm to improve stability bounds iteratively. Examples illustrate that less conservative bounds can be obtained, Compared with the existing results, they improve the stability bounds by 20 to 48% after only a few iterations.