Global stabilization of a class of cascaded systems with upper‐triangular structures

Abstract

In this paper, the global stabilization problem of a class of cascaded systems with upper-triangular structures is considered. On the basis of the forwarding technique, a series of virtual controllers are recursively constructed for the driving subsystem. According to the mild assumption imposed on the driven subsystem, a partial-state feedback controller is obtained for the entire cascaded nonlinear system by developing a delicate design fashion. It is shown that the obtained state feedback controller will render the entire cascaded nonlinear system globally asymptotically stable. Numerical examples are conducted to validate the proposed control scheme. /journal/rnc Int J Robust Nonlinear Control. 2018;28:4330-4344. LAN ET AL. 4331does not necessarily imply the stability of the nonlinear CSs. 1 Therefore, the control problem of nonlinear CSs is more challenging in the control field. Over the last two decades, various control methods have been developed for nonlinear CSs in the literature. * For the stabilization problem of nonlinear CSs, one intuitive idea to deal with this problem is to design full-state feedback controller that makes full use of the states information of the entire cascade systems. On the basis of the feedback passivation approach, a Lyapunov function construction and global controller design method is proposed in the work of Jankovic et al 2 for a class of nonlinear cascade and feedforward systems whose zero dynamics of the driven subsystem are globally stable. Then, this result is generalized in the work of Mazenc et al 15 by replacing the earlier growth conditions with a necessary boundedness condition in the construction of the Lyapunov function. Under the assumption that the zero dynamics of the driven subsystem are globally asymptotically stable and locally exponentially stable, a robust full-state feedback controller is constructed by using backstepping procedure in the work of Lin. 3 For a class of minimum-phase nonlinear CSs with unknown parameters, an adaptive regulation problem is investigated in the work of Lin and Qian 16 by using parameter separation technique and feedback domination approach. Another basic idea is to stabilize CSs by using partial-state feedback control approach, that is, only the driving subsystems' information is involved in the feedback controller design, whereas the driven subsystems' information is used in the stability analysis of the entire cascade system. On the basis of small gain theorem, 17 a stepwise constructive partial-state feedback control methodology is proposed in the work of Jiang and Marcels 4 for a class of nonlinear CSs in the context of input-to-state stability (ISS). 18 The robust global stabilization problem for a class of nonlinear CSs with dynamic uncertainty is considered in the work of Chen and Huang 6 by using Lyapunov's direct method. When the zero dynamics of the driven subsystem are ISS but not exponentially stable, a robust controller is constructed recursively for a class of polynomial CSs. 19 As the driven subsystem satisfies ...

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