Extended small gain theorem for time-delay switched systems control and closed-loop robustness enhancement

This paper generalises the Small Gain Theorem SGT to cope with switched linear systems. A switching strategy able to guarantee stability of the feedback interconnection of a switching linear subsystem and a linear stable norm-bounded perturbation is developed. the new version of SGT is specially important to solve two different problems. the first one concerns the possibility of enhancing the robustness of a feedback control system by appropriately orchestrating the switches among a set of given linear regulators. the second problem is the design of a stabilising switching strategy for time-delay switched systems. Both cases of state and output feedback switching laws are considered. Remarkably, since the sufficient conditions for the existence of a solution are delay-dependent, they are less conservative with respect to previous results in the literature. the theory is illustrated by means of academic examples.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)European Commission under the MoVeS projectUniversidade Federal de São Paulo, Inst Sci & Technol, BR-12231280 Sao Jose Dos Campos, SP, BrazilUniv Estadual Campinas, DSCE Sch Elect & Comp Engn, BR-13083852 Campinas, SP, BrazilCNR, Ist Matemat Applicata & Teconol Informat Enrico M, I-20133 Milan, ItalyPolitecn Milan, Dipartimento Elettron Informaz & Bioingn, I-20133 Milan, ItalyUniversidade Federal de São Paulo, Inst Sci & Technol, BR-12231280 Sao Jose Dos Campos, SP, BrazilEuropean Commission under the MoVeS project: FP7-ICT-2009-257005Web of Scienc