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              <p>This article proposes a three‐step interval estimation method in the framework of optimization for discrete‐time switched systems. The proposed method is realized based on the observers design via reachability analysis and measurement update. To obtain interval estimation, a peak‐to‐peak index is used to improve the robustness caused by disturbances and noise. The calculation of zonotopes and boxes is used for reachability analysis. A new iterative algorithm is proposed to reduce computational complexity. For improving estimation accuracy, a method of 1‐norm optimization is proposed, which can reduce the conservatism of computing intersections.</p>
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