In control theory, dynamical systems are in strict-feedback form when they can be expressed as
$$?\begin{array}{l}\dot{\mathbf{x}}=f_0(\mathbf{x})+g_0(\mathbf{x})z_1\\ {\dot{z}}_1=f_1\left(\mathbf{x},z_1\right)+g_1\left(\mathbf{x},z_1\right)z_2\\ {\dot{z}}_2=f_2\left(\mathbf{x},z_1,z_2\right)+g_2\left(\mathbf{x},z_1,z_2\right)z_3\\ ?\\ {\dot{z}}_i=f_i\left(\mathbf{x},z_1,z_2,\dots ,z_{i?1},z_i\right)+g_i\left(\mathbf{x},z_1,z_2,\dots ,z_{i?1},z_i\right)z_{i+1}\text{?for?}1\le i<k?1\\ ?\\ {\dot{z}}_{k?1}=f_{k?1}\left(\mathbf{x},z_1,z_2,\dots ,z_{k?1}\right)+g_{k?1}\left(\mathbf{x},z_1,z_2,\dots ,z_{k?1}\right)z_k\\ {\dot{z}}_k=f_k\left(\mathbf{x},z_1,z_2,\dots ,z_{k?1},z_k\right)+g_k\left(\mathbf{x},z_1,z_2,\dots ,z_{k?1},z_k\right)u\end{array}$$
where

• $\mathbf{x}\in {\mathbb{R}}^n$ with $n\ge 1$
• $z_1,z_2,\dots ,z_i,\dots ,z_{k?1},z_k$ are scalars,
• $u$ is a scalar input to the system, - $f_0,f_1,f_2,\dots ,f_i,\dots ,f_{k?1},f_k$ vanish at the origin (i.e., $f_i(0,0,\dots ,0)=0)$
• $g_1,g_2,\dots ,g_i,\dots ,g_{k?1},g_k$ are nonzero over the domain of interest (i.e., $g_i\left(\mathbf{x},z_1,\dots ,z_k\right)=0$ for $1\le i\le k)$

Here, strict feedback refers to the fact that the nonlinear functions $f_i$ and $g_i$ in the ${\dot{z}}_i$ equation only depend on states $x,z_1,\dots ,z_i$ that are fed back to that subsystem. ${}^{[1]}$ That is, the system has a kind of lower triangular form.

Reference: https://en.wikipedia.org/wiki/Strict-feedback_form

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