Corrigendum to published papers in Applied Mathematics and Computation

The authors appreciate Professor Cheng-De Zheng pointing errors in definition of LMI variable [1–8] and would like to correct an error in definition of an LMI variable of the paper [1–8]. In [1–8], Theorems or Corollaries present stability or stabilization criteria for the system with uncertainties or nonlinear perturbations. In [1–8], the LMI variables H in [1–3,5– 8], Hi ði 1⁄4 1;2Þ in [4], and P2 in Theorem 1 of [6] are defined as a positive matrix. However, the aforementioned LMI variables in [1–6] should be positive scalars. Then, all the Theorems and Proofs in [1–8] are still valid without any further changes. Note that the numerical results for systems without uncertainties ([1–3,5,6]) or nonlinear perturbations ([4]) do not change even though the H in [1–3,5–8], Hiði 1⁄4 1;2Þ in [4], and P2 in Theorem 1 of [6] are corrected to a positive scalar. In case that the system has uncertainties or nonlinear perturbations, the numerical results become to change a little. In [1], Example 2 considers the case with uncertainties. The corrected versions for Table 2 and 3 in [1] are given in Tables 1 and 2, respectively. Example 3 in [2] considers the system with uncertainties. The corrected versions for Tables 2–4 in [2] are shown in Tables 3–5, respectively. In [3], Example 2 considers the case with uncertainties. The corrected versions for Tables 2 and 3 in [3] are given in Tables 6 and 7, respectively. In [4], Example 1 and 2 consider the case with nonlinear perturbations. The corrected maximum allowable bound under the same condition in Example 1 is corrected to 2.8687 from 3.4039. The corrected result still gives larger delay bound than one of previous work given in Ref. [6] of paper [4]. And the corrected versions for Table 1 in [4] are given in Table 8. In [5], Example 1, 3, 4, 5, and 6 consider the case with uncertainties. The corrected versions for Tables 1–4, 6 and 7 in [5] are given in Tables 9–14, respectively. In [6], Example 1 and 3 consider the case with uncertainties. The corrected versions for Tables 1, 2 and 4 in [6] are given in Tables 15–17, respectively. In [7], the corrected results are given in Table 18. In [8], the corrected maximum allowable bound under a = 0, hL = 0 and unknown hD changes from 0.7245 to 0.6918, while is the result still larger than the ones of the previous works mentioned in [8]. Also, the corrected results for Tables 1 and 2 [8] are given in Tables 19 and 20, respectively.