Abstract
In this paper, we study the problem of stability robustness of two-dimensional discrete systems in a local state-space setting. Two methods are proposed for efficient numerical evaluation of the exact complex perturbation bound ν. The first method combines Byers' bisection method with a three-point-pattern optimization technique to compute ν. The second method utilizes a direct optimization technique to find the bound. In addition, a 2-D Lyapunov approach is proposed to obtain two lower bounds of ν, and numerical techniques for solving the constant 2-D Lyapunov equation involved are presented. The paper is concluded with an example illustrating the main results obtained.
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