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Section: New Results

Set Invariance for Descriptor Systems

Participants : Giorgio Valmorbida, Ye Wang [Universidade Federal do Rio Grande do Sul] , Sorin Olaru [L2S, CentraleSupélec] , Vicenç Puig [Universitat Politècnica de Catalunya] , Gabriela Cembrano [Universitat Politècnica de Catalunya] .

Some descriptor systems, characterized by a difference-algebraic relation, appear in economic systems. For such a class of systems we study robust invariant set characterizations of discrete-time descriptor systems and propose an active mode detection mechanism. The considered class of descriptor systems assumes regularity, stability and is affected by unknown-but-bounded disturbances.

As a first theoretical result, we establish a general framework for robust invariant sets for discrete-time descriptor systems in both causal and non-causal cases. Particular transformations are subsequently proposed for handling causal and non-causal descriptor systems and will be used to characterize the effects of disturbances. Based on these set-theoretic notions and a designed input signal for active set separations, we propose an active mode detection mechanism by exploiting the strong invariance properties.