Algorithm 1: Asynchronous switching control gain matrix based on DETM

Input: The matrices ${\mathit{H}}_{\sigma }$, $\mathit{A},\mathit{B}$, related parameters of ADT and DETM Output: Controller gain matrices ${\mathit{K}}_{\sigma }$ 1Step 1: Compute transformation matrices ${\mathit{U}}_{\sigma \left(t\right)}$ and ${\mathsf{\Lambda }}_{\sigma \left(t\right)}$, then obtain ${\lambda }_{ip}$ 2Step 2: Validate ${\rho }_2{\lambda }_{ip}^2-{\rho }_1<0$ 3Step 3: Solve LMIs ${\mathbf{\Xi }}_{i1}<0,{\mathbf{\Xi }}_{i2}<0$, then obtain matrices $\mathit{Q}$ and ${\mathit{Y}}_p$ 4Step 4: Ensure ${\mathit{Q}}_{ip}<\mu {\mathit{Q}}_{iq}$ and $c{\rho }_2{\lambda }_{ip}^2\mathit{I}-{\lambda }_{ip}{\mathit{Y}}_q^T{\mathit{B}}^T>0$ 5Step 5: Compute control gain matrix ${\mathit{K}}_p={\mathit{Y}}_p{\mathit{Q}}^{-1}$