Nonsmooth Decentralized Stabilization for Interconnected Systems Subject to Strongly Coupled Uncertain Interactions

Abstract

This paper revisits the decentralized stabilization problem for a class of interconnected nonlinear systems subject to strongly coupled uncertain interactions. As a main contribution, we show that, without any priori required restrictive nonlinear growth conditions, a ${\mathcal {C}}^{1}$ condition of the nonlinear interactions is sufficient to derive a finite-time convergent decentralized stabilizing control law under a semi-global control objective. Another new feature is the adoption of a novel one step nonsmooth synthesis method which leads to a simple form of stabilizing control law with easily implementable gain tuning mechanisms. A numerical example and its simulation verification are provided to illustrate the simplicity and effectiveness of the proposed method.