$L_p$-stabilization of integrator chains subject to input saturation using Lyapunov-based homogeneous design

Yacine Chitour, Mohamed Harmouche, Salah Laghrouche

Consider the $n$-th integrator $\dot{x}=J_{n}x+\sigma (u)e_n$, where $x\in {\mathbb{R}}^n$, $u\in \mathbb{R}$, $J_n$ is the $n$-th Jordan block and $e_n=(0\cdots 01{)}^T\in {\mathbb{R}}^n$. We…