Decentralized $H_{\infty }$ Control for Switched Interconnected Large-Scale Systems: A Computationally Attractive Method

Abstract

This article investigates the decentralized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controller design problems for switched interconnected large-scale systems (ILSSs). The designed decentralized controllers are dependent on the switching modes which can reduce the conservatism. Sufficient conditions are established for ensuring the asymptotic stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance of the studied switched ILSSs. Novel computationally attractive mode-dependent controller deign method is derived. The established controller design conditions eliminate the computationally expensive matrix inversion terms and are given in terms of linear matrix inequalities. Finally, the validness of the proposed decentralized controller design method is verified by the interconnected continuous stirred-tank reactor systems. Other three numerical examples are also performed to show the advantages and superiorities of the derived theoretical results.