Disturbance attenuation for uncertain nonlinear cascaded systems (Q1883956)

The paper investigates the almost disturbance decoupling (ADD) with internal stability for a class of single-input single-output high-order lower-triangular nonlinear systems described by equations of the form \[ \left\{\begin{aligned} \dot x_1=&x_2^{p_1}+f_1(x_1,t)+\phi_1(x_1,t)w,\\ &\dots\\ \dot x_i=&x_{i+1}^{p_i} + f_i(x_1,\dots,x_i,t) +\phi_i(x_1,\dots ,x_i,t)w,\\ &\dots\\ \dot x_n=&u^{p_n} + f_n(x_1,\dots,x_n,t) +\phi_n(x_1,\dots ,x_n,t)w,\\ y=&h(x_1), \end{aligned}\right. \] where \(u\in\mathbb R\) is the control input, \(y\in\mathbb R\) the system output, and \(w\in\mathbb R^s\) the disturbance signal, \(p_i\) are positive integers and \(f_i(\cdot)\), \(\phi_i(\cdot)\) are unknown smooth functions, \(i =~\!\!1,2,\dots,n\), while \(h(\cdot)\) is a known smooth function and \(h(0) = 0\). Based on the adding one power integrator technique and recursive design, a constructive solution to the ADD problem under growth conditions which are a natural generalization of the feedback linearization condition is presented. The new design technique really generalizes the well-known design technique called adding a linear integrator.