WIAS Preprint No. 555, (2000)

Duality principle for discrete linear inclusions


  • Vladimirov, Alexander A.

2010 Mathematics Subject Classification

  • 58E35 47H30


  • Matrix product, stability, oblique projection, Skorokhod problem




Two properties of finite sets {Aj} of n x n-matrices are introduced: P-stability and BV-stability. These properties can be interpreted as two kinds of robustness of orbits of the form xi+1 = Ajixi + ui with respect to disturbances {ui}. Duality between these properties is established, which proves that they are equivalent, respectively, to the right convergent product (RCP) property and the left convergent product (LCP) property of finite sets of matrices. The results can be applied, in particular, in the theory of polyhedral Skorokhod problems and sweeping processes with oblique reflection.

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