New results on quadratic stabilization of switched linear systems with polytopic uncertainties

^** Corresponding author. Email: longwang{at}pku.edu.cn^*** Email: jizj{at}mech.pku.edu.cn In this paper, the quadratic stabilization of switched linearsystems with polytopic uncertainties is considered. Comparedwith the existing result, a more general switching control methodis proposed to guarantee the quadratic stabilization. This switchingcontrol method is based on the partition of the vertex matrixset of each subsystem. By this method, the matrix inequalitiesneeded to be solved are always less than those needed to besolved before except one extreme case; for this case, it isequal. The switched control synthesis problem is also studiedfor both switched state feedback and output feedback. Severalbilinear matrix inequality based conditions are derived forboth cases.