Trapezoidal wave rms value calculation
Well, the general formula for the RMS-voltage is given by:
$$\overline{\text{I}}=\sqrt{\frac{1}{\text{T}}\int_0^\text{T}\left(\text{I}\left(t\right)\right)^2\space\text{d}t}\tag1$$
So, in your case:
$$\overline{\text{I}}=\sqrt{\frac{1}{\text{T}_\text{on}+\text{T}_\text{off}}\cdot\left\{\int_0^{\text{T}_\text{on}}\left(-\text{I}_0\right)^2\space\text{d}t+\int_0^{\text{T}_\text{off}}\left(\text{I}_\text{a}+\frac{\text{I}_\text{b}-\text{I}_\text{a}}{\text{T}_\text{off}}\cdot t\right)^2\space\text{d}t\right\}}\tag2$$