In [24], a semi-active controller is formulated for a vibrating structure. The Lyapunov analysis is combined with passivity theory and uses a storage function as a Lyapunov function. The BIBO stability result relates the displacements and velocities as a function of L\({}_{2}\) external forces. Also, the ranges of the controller parameters that lead to BIBO stability are defined. In [25], a robust observer-based controller design is formulated for a class of nonlinear systems described by Tagaki-Sugeno (TS) models, subject to persistent bounded external disturbance. A non-quadratic Lyapunov function is used. The BIBO stability result relates the closed loop states as a function of the external disturbance. In [26], an adaptive neural controller is developed for a n-link rigid robotic manipulator. Neural networks are used for approximating the unknown dynamics, and the backstepping strategy is used as a basic control framework. As a result of the controller design, the overall Lyapunov function (V\({}_{2}\)) comprises the subsystem Lyapunov functions associated to the z\({}_{i}\) states and the parameter updating error. The dV\({}_{2}\)/dt expression is a function of V\({}_{2}\), so that it is concluded that the z\({}_{i}\) states converge to compact sets whose width depends on the neural approximation error. In this paper, we study the stability of a network model comprising three CSTRs with the following features: (i) the pollutant concentration in the inflow to the first CSTR is time varying; (ii) the first and second CSTRs are connected in series, whereas the second and third CSTRs are connected in parallel with flow exchange; (iii) the states converge to a compact set instead of an equilibrium point. The practical applicability of the arrangement of CSTRs is to provide a simpler model of pollution removal from wastewater treatment via constructed wetlands, generating a satisfactory description of experimental pollution values with a satisfactory transport dead time. The aforementioned features make the global stability analysis complex. The convergence sets of the system states are determined as a function of the concentration of the inflow to the first tank, and the global asymptotic convergence of the states to these sets and their invariant nature are proved. Also, the effect of the presence of flow exchange on the transient value of the system states is determined, and it is concluded that it has no effect on the convergence regions. The study is based on global stability using dead zone Lyapunov functions and Barbalat's lemma. The contribution of this work with respect to closely related studies on global stability of continuous stirred tank reactors (CSTR) are:  
* we consider three connected CSTRs, including a side CSTR with flow exchange, whereas related studies consider a single CSTR with several states (e.g., biomass and substrate concentrations) [20; 21; 29; 30];
* we consider the case that the system converges to a compact set, whereas related studies consider convergence to an equilibrium point [20; 21; 29; 30]. The paper is organized as follows. The preliminaries and description of the model are presented in Section 2; the stability analysis is presented in Section 3, including the first tank (Section 3.1) and both the second and third tanks (Section 3.2). The numerical simulation is presented in Section 4, and the conclusions in Section 5.