Jankovic, Mrdjan; Sepulchre, Rodolphe; Kokotovic, Petar V. Constructive Lyapunov stabilization of nonlinear cascade systems. (English) Zbl 0869.93039 IEEE Trans. Autom. Control 41, No. 12, 1723-1735 (1996). Consider the system \[ \dot x= f(x)+h(x,\xi),\quad f(0)=0,\quad h(x,0)\equiv 0,\quad\dot\xi= A\xi\tag{1} \] with \(A\) a Hurwitz matrix. The authors consider a Lyapunov function of the form \(V_0(x,\xi)= W(x)+ \psi(x,\xi)+\xi^*P\xi\), where the cross term \(\psi\) is constructed in such a way that \(V_0(x,\xi)>0\) is radially unbounded and nonincreasing along the trajectories. This is the main step in the global stabilization of systems with input obtained by various augmentations of (1) such as \[ \dot x= f(x)+h(x,\xi)+ g_1(x,\xi)u,\quad\dot\xi= A\xi+bu,\tag{2} \]\[ \dot x= f(x)+h(x,\xi)+ g_2(x,\xi,y)y,\quad\dot\xi= A\xi+by,\quad\dot y=u\tag{3} \] and \[ \dot z= \varphi(z)+ \kappa(z,x,\xi)+ \rho(z,x,\xi)u,\quad\dot x= f(x)+h(x,\xi)+ g(x,\xi)u,\quad\dot\xi= A\xi+bu.\tag{4.} \] Reviewer: V.Răsvan (Craiova) Cited in 57 Documents MSC: 93D15 Stabilization of systems by feedback 93A99 General systems theory 93D30 Lyapunov and storage functions 93C10 Nonlinear systems in control theory Keywords:nonlinear systems; Lyapunov function; global stabilization PDFBibTeX XMLCite \textit{M. Jankovic} et al., IEEE Trans. Autom. Control 41, No. 12, 1723--1735 (1996; Zbl 0869.93039) Full Text: DOI Link