Set-invariance characterizations of discrete-time descriptor systems with application to active mode detection

Abstract : In this paper, we study robust invariant set characterizations of discrete-time descriptor systems and propose an active mode detection mechanism for discrete-time descriptor systems considering multiple modes of operation. 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.
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Ye Wang, Sorin Olaru, Giórgio Valmórbida, Vicenç Puig, Gabriela Cembrano. Set-invariance characterizations of discrete-time descriptor systems with application to active mode detection. Automatica, Elsevier, 2019, 107, pp.255-263. ⟨10.1016/j.automatica.2019.05.053⟩. ⟨hal-02430209⟩

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