Abstract
In this study, a polyhedral approximation method for reachable sets of linear delay systems is investigated. For a continuous linear system with multiple delays, the first Euler scheme combining with linear interpolation is used to transform it into a discrete one. Then a polyhedral approximation method based on optimisation techniques is proposed to compute the discrete reachable set. By specifying an approximation error and solving a finite number of convex optimisation problems, a polyhedron can be constructed as the approximation of the discrete reachable set. The approximation quality measured in Hausdorff distance can be directly controlled. Next, illustrated examples are given to demonstrate the effectiveness of the proposed method. Finally, the authors show some reachable sets of linear delay control systems, and they compare the proposed method with some other methods in the literature. Numerical results clearly show the superior performance of the proposed method.
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