Decentralized uniform finite‐time stabilization of large‐scale nonlinear networks by small‐gain theorems

Abstract

AbstractWe solve the problem of decentralized uniform finite‐time stabilization for a large‐scale network of nonlinear systems in triangular form which are not feedback linearizable and whose input–output maps are not invertible. For this, we provide a new recursive design to satisfy the conditions of a certain modification of the small‐gain theorems for the case of the uniform finite‐time stability of large‐scale networks. In the general case, we consider the general triangular form systems whose input–output links are surjections only. In addition, we consider the special case of the triangular form systems with polynomial integrators, which is also needed as the first step of the proof of our main result. In the latter case, the design becomes constructive, the decentralized stabilizers can be designed explicitly, and this is demonstrated by examples.