1 Correction to: Circuits, Systems, and Signal Processing https://doi.org/10.1007/s00034-018-0839-z

The original version of the article unfortunately contained typographical errors in unnumbered equations before (12). The correct equations should be

$$\begin{aligned} \int _{-\frac{h_{1}}{m}}^{0}\int _{t_{1}+\beta }^{t_{1}}\dot{x}^{hT}(\alpha )Q_{3}^{h}\dot{x}^{h}(\alpha )d\alpha d\beta\ge & {} 2\left( \begin{array}{c} x^{h}-\displaystyle \frac{m}{h_{1}}\int _{t_{1}-\frac{h_{1}}{m}}^{t_{1}}x^{h}(\alpha )d\alpha \\ \end{array} \right) ^{T}Q_{3}^{h} \\&\times \left( \begin{array}{c} x^{h}-\displaystyle \frac{m}{h_{1}}\int _{t_{1}-\frac{h_{1}}{m}}^{t_{1}}x^{h}(\alpha )d\alpha \\ \end{array} \right) ,\\ \int _{-\frac{h_{2}}{m}}^{0}\int _{t_{2}+\beta }^{t_{2}}\dot{x}^{vT}(\alpha )Q_{3}^{v}\dot{x}^{v}(\alpha )d\alpha d\beta\ge & {} 2\left( \begin{array}{c} x^{v}-\displaystyle \frac{m}{h_{2}}\int _{t_{2}-\frac{h_{2}}{m}}^{t_{2}}x^{v}(\alpha )d\alpha \\ \end{array} \right) ^{T}Q_{3}^{v}\\&\times \left( \begin{array}{c} x^{v}-\displaystyle \frac{m}{h_{2}}\int _{t_{2}-\frac{h_{2}}{m}}^{t_{2}}x^{v}(\alpha )d\alpha \\ \end{array} \right) ,\\ \end{aligned}$$
$$\begin{aligned}&\int _{-\frac{h_{1}}{m}}^{0}\int _{\lambda }^{0}\int _{t_{1}+\beta }^{t_{1}}\dot{x}^{hT}(\alpha )Q_{4}^{h}\dot{x}^{h}(\alpha )d\alpha d\beta d\lambda \\&\quad \ge \frac{6h_{1}}{m}\left( \begin{array}{c} \displaystyle \frac{1}{2}x^{h}-\frac{m^{2}}{h_{1}^{2}}\int _{-\frac{h_{1}}{m}}^{0}\int _{t_{1}+\beta }^{t_{1}}x^{h}(\alpha )d\alpha d\beta \end{array} \right) ^{T}Q_{4}^{h}\\&\qquad \times \left( \begin{array}{c} \displaystyle \frac{1}{2}x^{h}-\frac{m^{2}}{h_{1}^{2}}\int _{-\frac{h_{1}}{m}}^{0}\int _{t_{1}+\beta }^{t_{1}}x^{h}(\alpha )d\alpha d\beta \end{array} \right) ,\\&\int _{-\frac{h_{2}}{m}}^{0}\int _{\lambda }^{0}\int _{t_{2}+\beta }^{t_{2}}\dot{x}^{vT}(\alpha )Q_{4}^{v}\dot{x}^{v}(\alpha )d\alpha d\beta d\lambda \\&\quad \ge \frac{6h_{2}}{m}\left( \begin{array}{c} \displaystyle \frac{1}{2}x^{v}-\frac{m^{2}}{h_{2}^{2}}\int _{-\frac{h_{2}}{m}}^{0}\int _{t_{2}+\beta }^{t_{2}}x^{v}(\alpha )d\alpha d\beta \end{array} \right) ^{T}Q_{4}^{v}\\&\qquad \times \left( \begin{array}{c} \displaystyle \frac{1}{2}x^{v}-\frac{m^{2}}{h_{2}^{2}}\int _{-\frac{h_{2}}{m}}^{0}\int _{t_{2}+\beta }^{t_{2}}x^{v}(\alpha )d\alpha d\beta \\ \end{array} \right) ,\\&\displaystyle \int _{-\frac{h_{1}}{m}}^{0}\int _{\delta }^{0}\int _{\lambda }^{0}\int _{t_{1}+\beta }^{t_{1}}\dot{x}^{hT}(\alpha )Q_{5}^{h}\dot{x}^{h}(\alpha )d\alpha d\beta d\lambda d\delta \\&\quad \ge \frac{24h_{1}^{2}}{m}\left( \begin{array}{c} \displaystyle \frac{1}{6}x^{h}-\frac{m^{3}}{h_{1}^{3}}\int _{-\frac{h_{1}}{m}}^{0}\int _{\lambda }^{0}\int _{t_{1}+\beta }^{t_{1}}x^{h}(\alpha )d\alpha d\beta d \lambda \end{array} \right) ^{T}Q_{5}^{h}\\&\qquad \times \left( \begin{array}{c} \displaystyle \frac{1}{6}x^{h} -\frac{m^{3}}{h_{1}^{3}}\int _{-\frac{h_{1}}{m}}^{0}\int _{\lambda }^{0}\int _{t_{1}+\beta }^{t_{1}}x^{h}(\alpha )d\alpha d\beta d \lambda \\ \end{array} \right) ,\\&\displaystyle \int _{-\frac{h_{2}}{m}}^{0}\int _{\delta }^{0}\int _{\lambda }^{0}\int _{t_{2}+\beta }^{t_{2}}\dot{x}^{vT}(\alpha )Q_{5}^{v}\dot{x}^{v}(\alpha )d\alpha d\beta d\lambda d\delta \\&\quad \ge \frac{24h_{2}^{2}}{m}\left( \begin{array}{c} \displaystyle \frac{1}{6}x^{v}-\frac{m^{3}}{h_{2}^{3}}\int _{-\frac{h_{2}}{m}}^{0}\int _{\lambda }^{0}\int _{t_{2}+\beta }^{t_{2}}x^{v}(\alpha )d\alpha d\beta d\lambda \end{array} \right) ^{T}Q_{5}^{v}\\&\qquad \times \left( \begin{array}{c} \displaystyle \frac{1}{6}x^{v} -\frac{m^{3}}{h_{2}^{3}}\int _{-\frac{h_{2}}{m}}^{0}\int _{\lambda }^{0}\int _{t_{1}+\beta }^{t_{2}}x^{v}(\alpha )d\alpha d\beta d \lambda \\ \end{array} \right) , \end{aligned}$$