Nonlinear Dyn (2012) 67:2847–2856 DOI 10.1007/s11071-011-0193-1 ORIGINAL PAPER On the global stabilization of Takagi–Sugeno fuzzy cascaded systems N. Hadj Taieb · M.A. Hammami · F. Delmotte · M. Ksontini Received: 7 January 2011 / Accepted: 3 August 2011 / Published online: 15 September 2011 © Springer Science+Business Media B.V. 2011 Abstract This paper deals with the problem of the global stabilization for a class of cascade nonlinear control systems. It is well known that, in general, the global asymptotic stability of the cascaded sub- systems does not imply the global asymptotic stabil- ity of the composite closed-loop system. In this pa- per, we give additional sufficient conditions for the global stabilization of a cascade nonlinear system. In particular, we consider a class of Takagi–Sugeno (TS) fuzzy cascaded systems. Using the so-called parallel distributed compensation (PDC) controller, we prove that this class of systems can be globally asymptoti- cally stable. An illustrative example is given to show the applicability of the main result. Keywords Fuzzy systems · PDC controller · Cascaded systems · Lyapunov stability N.H. Taieb · M.A. Hammami ( ) Faculty of Sciences of Sfax, Department of Mathematics, University of Sfax, Sfax, Tunisia e-mail: MohamedAli.Hammami@fss.rnu.tn N.H. Taieb e-mail: nizar.hadjtaieb@yahoo.fr F. Delmotte University of Artois, Arras, France e-mail: francois.delmotte@univ-artois.fr M. Ksontini Sfax Preparatory Institute for Engineering Studies, Sfax, Tunisia e-mail: mohamedksantini@yahoo.fr 1 Introduction This work studies the problem of the global stabiliza- tion of nonlinear cascaded systems of the form  ˙ x 1 = f (x 1 ,x 2 ) ˙ x 2 = g(x 1 ,x 2 , u) (1.1) where x 1 ∈ R n ,x 2 ∈ R q and u ∈ R m . The functions f and g are supposed C ∞ and to satisfy f(0, 0) = 0, g(0, 0, 0) = 0. Let ˙ x 1 = f (x 1 ,x 2 ). (1.2) It is well known that if the differential equation ˙ x 1 = f (x 1 , 0) (1.3) has x 1 = 0 as an equilibrium point globally asymptot- ically stable, if the system ˙ x 2 = g(x 1 ,x 2 , u) (1.4) is globally asymptotically stabilized at the origin, uni- formly on x 1 by a feedback law u(x 1 ,x 2 ), and if all the orbits of the closed-loop system  ˙ x 1 = f (x 1 ,x 2 ) ˙ x 2 = g(x 1 ,x 2 , u(x 1 ,x 2 )) are bounded, then (x 1 ,x 2 ) = (0, 0) is an equilibrium point globally asymptotically stable for (1.1)[13, 15].