LMI approach to <i>L</i> ₂ -gain analysis and control synthesis of uncertain switched systems

Abstract

L2-gain analysis is used to characterise conditions under which an uncertain switched system is uniformly quadratically stable (UQS) with an L2-gain smaller than a constant γ. The control synthesis is to design switched-state feedback and switched output feedback controllers, guaranteeing that the corresponding closed-loop system is UQS with an L2-gain smaller than a constant γ. All the results are expressed in terms of linear matrix inequalities, which can be easily tested with efficient algorithms.