The "trick" is to preserve the identities of the lags in the transition matrix. The corresponding block of the transition matrix (for some state variable $x$) becomes:

 $$ \begin{bmatrix} x_t \\ x_{t-1}\\ x_{t-2}\\ \vdots\\ x_{t-20}\\ \end{bmatrix} = \begin{pmatrix} a & 0 & \cdots && 0\\ 1 & 0 & \cdots && 0\\ 0 & 1 & 0 \cdots && 0\\ \vdots & & \ddots && \vdots\\ 0 & \dots & 0 & 1 & 0 \end{pmatrix} \begin{bmatrix} x_{t-1} \\ x_{t-2}\\ x_{t-3}\\ \vdots\\ x_{t-21}\\ \end{bmatrix} $$ The $a$ coefficient captures the one-period transition for $x$ from $t-1$ to $t$. The 1-coefficients carry the lags over to the next period as they are. The $a$ coefficient will be estimated and determines $x_t$, but the ones are imposed, and so are not estimated. Note that the lag 21, which you don't want, has a zero coefficient and is not carried along.

See, for example, appendix B in Banbura, Marta and Giannone, Domenico and Reichlin, Lucrezia, Nowcasting (November 30, 2010). ECB Working Paper No. 1275

The "trick" is to preserve the identities of the lags in the transition matrix. In period $t$, you have (for some state variable $x$) $$ x_t =a x_{t-1} \\ x_{t-1} = x_{t-1}\\ x_{t-2} = x_{t-2}\\ \cdots $$ So, the corresponding block of the transition matrix becomes:  $$ \begin{bmatrix} x_t \\ x_{t-1}\\ x_{t-2}\\ \vdots\\ x_{t-20}\\ \end{bmatrix} = \begin{pmatrix} a & 0 & \cdots && 0\\ 1 & 0 & \cdots && 0\\ 0 & 1 & 0 \cdots && 0\\ \vdots & & \ddots && \vdots\\ 0 & \dots & 0 & 1 & 0 \end{pmatrix} \begin{bmatrix} x_{t-1} \\ x_{t-2}\\ x_{t-3}\\ \vdots\\ x_{t-21}\\ \end{bmatrix} $$ The $a$ coefficient captures the one-period transition for $x$ from $t-1$ to $t$. This coefficient may or may not be estimated. Note that lag 21, which you don't want, has a zero coefficient and is not carried along.

See, for example, appendix B in Banbura, Marta and Giannone, Domenico and Reichlin, Lucrezia, Nowcasting (November 30, 2010). ECB Working Paper No. 1275