It can be verified that the system (21) does not satisfy the condition of [4] and, hence, no conclusion on the global asymptotic stability can be drawn based on the results of [4]. However, by using Algorithm 3, it can be verified that the condition of Theorem 2 is satisfied with P = 0:5643 00:3214 02:5945We thus conclude that (21) is globally asymptoticallystable at the origin. A trajectory is shown in Fig. 4. IV. CONCLUSIONIn this note, we established simple conditions under which linear systems defined on a closed hypercube and linear systems with partial state saturation are globally asymptotically stable at the origin. These conditions were shown to be less conservative than the existing conditions. Based on these conditions, iterative LMI algorithms are proposed for verifying global asymptotic stability of these systems. Numerical examples were used to show the effectiveness of the proposed algorithms. REFERENCES[1] S.

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