Multiple integral inequality and its applications to decentralised control of large-scale systems with time-varying delays and unknown saturated inputs

As the main objective of this study, a new multiple integral inequality is proposed. By combining this multiple integral inequality with adaptive approach, some simple design methods can be developed to synthesise the decentralised adaptive robust control schemes for a rather large class of uncertain large-scale interconnected systems. As an application of the proposed multiple integral inequality to decentralised control theory, the problem of decentralised robust stabilisation is also considered for a class of uncertain large-scale interconnected systems with both time-varying delays and saturated input non-linearities. It is shown that this multiple integral inequality can well deal with the interconnection terms of large-scale systems. In particular, based on the proposed multiple integral inequality, the time-varying delays can be assumed to be any continuous and bounded non-negative functions in time which are not required that their derivatives have to be less than one, and it is also not required for any information on the saturated input non-linearities to be known. A numerical example and the corresponding simulations are also given to illustrate the validity of the theoretical results.