Vector incremental L_2-gain and incremental stability for switched nonlinear systems

摘要

This paper studies vector incremental L-2-gain and incremental stability for switched nonlinear systems using individual incremental gains and multiple storage functions. Firstly, a vector incremental L-2-gain concept for switched nonlinear systems is proposed. Each subsystem is not required to have incremental L-2-gain, but it has its own incremental L-2-gain and the related storage function, when it is active. The transformation of "energy" from the active subsystem to each inactive subsystem is characterized by cross-supply rates. Then, we show that a switched nonlinear system who has vector incremental L-2-gain can be incrementally stabilized under some constraints on the energy change of inactive subsystems. Secondly, a state-dependent switching law is designed to achieve vector incremental L-2-gain, even if each subsystem does not have incremental L-2-gain in the classic sense. Thirdly, each switched system is not required to have vector incremental L-2-gain, but the feedback interconnection of switched nonlinear systems is incrementally stabilized by the design of a composite switching law. The switching law allows the two switched systems switch asynchronously. Two examples are provided to verify the effectiveness of the proposed method. (c) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.