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Abstract: This paper considers the control problem of a class of uncertain switched systems defined on polyhedral sets known as piecewise linear systems where, instead of the conventional Caratheodory solutions, Filippov solutions are studied. In other words, in contrast to the previous studies, solutions with infinite switching in finite time along the facets and on faces of arbitrary dimensions are also taken into account. Firstly, established upon previous studies, a set of linear matrix inequalities are brought forward which determines the asymptotic stability of piecewise linear systems with Filippov solutions. Subsequently,  bilinear  matrix  inequality  conditions  for  synthesizing  a  robust  controller  with  a guaranteed H1 performance are presented. Furthermore, these results has been generalized to the case  of  piecewise  affine  systems.  Finally,  a  V–K  iteration  algorithm  is  proposed  to  deal  with  the aforementioned bilinear matrix inequalities. The validity of the proposed method is verified through the analysis of two simulation examples.

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