Correction to: Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

1 Correction to: Soft Computing https://doi.org/10.1007/s00500-022-06973-5

• 1. In page 7 at the right column, before Eq. (29),

  where $\Omega_{2.1} = diag\left\{ {\xi_{1} ,\xi_{2} } \right\}, \;\Omega_{2.2} = diag\left\{ {\hat{O}_{1}, \hat{O}_{2} } \right\},\;\Omega_{2.3} = diag\left\{ {\alpha e^{{ - \alpha T_{1} }} \eta_{1} ,0} \right\}$

  There are double commas in matrix $\Omega_{2.2}$, it must be $\Omega_{2.2} = diag\left\{ {\hat{O}_{1} , \hat{O}_{2} } \right\}$

• 2. At the top of page 8 in the left column, the symbols $\psi_{2.3}$ and $\psi_{3.1}$ should be $\Psi_{2.3}$ and $\Psi_{3.1}$, respectively. Please, modify them.

• 3. At the top of page 8 in the left column, there are some mistakes in the content of the matrix ‘‘$\Psi_{3.1}$’’. It should be:

  $$ \Psi_{3.1} = \left[ {\begin{array}{*{20}l} { - sym\left\{ {\hat{O}_{3} } \right\} + \tau \xi_{3} } \hfill & { 0} \hfill & 0 \hfill \\ { *} \hfill & { - \Lambda } \hfill & 0 \hfill \\ { *} \hfill & { *} \hfill & { - \psi_{1} } \hfill \\ \end{array} } \right] $$

• 4. In page 8 at the left column, please adjust the editing of the 3rd and 4th columns for the matrix ‘‘$\Psi_{3.3}$’’ to be aligned in the center as:

  $$ \left[ {\begin{array}{*{20}c} { - sym\left\{ {\rho_{1} } \right\} + \xi_{1} + \xi_{2} } & 0 & 0 & 0 \\ * & { - sym\left\{ {\rho_{2} } \right\} + \mu } & 0 & 0 \\ * & * & { - \eta_{2} \left( {1 - \lambda } \right)e^{ - \beta \tau } } & 0 \\ * & * & * & { - \mu \left( {1 - \lambda } \right)e^{ - \gamma \tau } } \\ \end{array} } \right] $$

• 5. In page 8 at the left column, please transfer the matrix ‘‘$\Psi_{3.2}$’’ to be before the matrix ‘‘$\Psi_{3.3}$’’.

• 6. At the top of page 10 in the left column,

  $\tilde{\Psi }_{1} = \left[ {\begin{array}{*{20}l} {\tilde{\Psi }_{1.1} } \hfill & {\tilde{\Psi }_{1.2} } \hfill \\ { *} \hfill & {\tilde{\Psi }_{1.3} } \hfill \\ \end{array} } \right],\widetilde{\Psi }_{2} = \left[ {\begin{array}{*{20}l} {\tilde{\Psi }_{2.1} } \hfill & {\tilde{\Psi }_{2.2} } \hfill \\ 0 \hfill & {\tilde{\Psi }_{2.3} } \hfill \\ \end{array} } \right],\tilde{\Psi }_{3} = \left[ {\begin{array}{*{20}l} {\tilde{\Psi }_{3.1} } \hfill & {\tilde{\Psi }_{3.2} } \hfill \\ { *} \hfill & {\tilde{\Psi }_{3.3} } \hfill \\ \end{array} } \right]$

  The editing of the symbol ‘‘$\widetilde{\Psi }_{2}$’’ must be ‘‘$\tilde{\Psi }_{2}$’’, where there is a big distance between ‘‘$\Psi_{2}$’’ and the tilde symbol ‘‘$\tilde{ }$’’.

  Please, adjust this editing $\widetilde{\Psi }_{2} = \left[ {\begin{array}{*{20}l} {\tilde{\Psi }_{2.1} } \hfill & {\tilde{\Psi }_{2.2} } \hfill \\ 0 \hfill & {\tilde{\Psi }_{2.3} } \hfill \\ \end{array} } \right]$ to be $\tilde{\Psi }_{2} = \left[ {\begin{array}{*{20}l} {\tilde{\Psi }_{2.1} } \hfill & {\tilde{\Psi }_{2.2} } \hfill \\ 0 \hfill & {\tilde{\Psi }_{2.3} } \hfill \\ \end{array} } \right]$.

• 7. If possible, transfer Fig. 7 and Fig. 8 to be before the conclusions section.

• 8. In page 7, after Eq. (29), the font of matrix $\Psi_{1.1}$ is small with respect to the other matrices ($\Psi_{1.2} ,\Psi_{1.3} , \ldots$), please, adjust the editing of this matrix.

• 9. At the bottom of page 7 in the right column,

  $$ \begin{aligned} \Psi_{2.1} & = \left[ {\begin{array}{*{20}l} { - \rho_{2} A_{di} + \hat{O}_{3}^{T} } \hfill & {B_{i} {\mathcal{Z}}_{2j} } \hfill & {B_{i} {\mathcal{Z}}_{3j} } \hfill \\ { \rho_{2} A_{di} } \hfill & 0 \hfill & { 0} \hfill \\ { 0} \hfill & {\omega_{a} \rho_{3} } \hfill & { 0} \hfill \\ \end{array} } \right], \Psi_{2.2} \\ & = \left[ {\begin{array}{*{20}c} {\rho_{1} A_{i} - B_{i} {\mathcal{Z}}_{2j} C_{i} } & 0 & {\begin{array}{*{20}c} 0 & 0 \\ \end{array} } \\ 0 & {\rho_{2} A_{i} - {\mathcal{Z}}_{1i} C_{i} } & {\begin{array}{*{20}c} 0 & 0 \\ \end{array} } \\ 0 & 0 & {\begin{array}{*{20}c} 0 & 0 \\ \end{array} } \\ \end{array} } \right] \\ \end{aligned} $$

  Please, transfer the symbol $\Psi_{2.2}$ to the next line to be:

  $$ \Psi_{2.1} = \left[ {\begin{array}{*{20}l} { - \rho_{2} A_{di} + \hat{O}_{3}^{T} } \hfill & {B_{i} {\mathbf{\mathcal{Z}}}_{2j} } \hfill & {B_{i} {\mathbf{\mathcal{Z}}}_{3j} } \hfill \\ { \rho_{2} A_{di} } \hfill & 0 \hfill & { 0} \hfill \\ { 0} \hfill & {\omega_{a} \rho_{3} } \hfill & { 0} \hfill \\ \end{array} } \right], $$
  $$ \Psi_{2.2} = \left[ {\begin{array}{*{20}c} {\rho_{1} A_{i} - B_{i} {\mathbf{\mathcal{Z}}}_{2j} C_{i} } & 0 & {\begin{array}{*{20}c} 0 & 0 \\ \end{array} } \\ 0 & {\rho_{2} A_{i} - {\mathbf{\mathcal{Z}}}_{1i} C_{i} } & {\begin{array}{*{20}c} 0 & 0 \\ \end{array} } \\ 0 & 0 & {\begin{array}{*{20}c} 0 & 0 \\ \end{array} } \\ \end{array} } \right] $$

• 10. In page 11, the font of the Eqs. (52, 53, 54, 55, and 56) is small with respect to the other equations. Please, adjust the editing of these equations.

• 11. At the bottom of page 11 in the left column, the font of the matrices $A_{1} ,A_{d1} ,$ and $A_{2}$ is small with respect to matrix $A_{d2}$. Please, adjust the editing of these matrices.

The original article has been corrected.