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

Ye Wang (1) , Sorin Olaru (2) , Giórgio Valmórbida (2, 3) , Vicenç Puig (4) , Gabriela Cembrano (5)

1 HRBEU - Harbin Engineering University
2 L2S - Laboratoire des signaux et systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
4 ESAII - Departament d'Enginyeria de Sistemes, Automàtica i Informàtica Industriall [Barcelona]
5 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]

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.

Mots clés: Robust invariant sets; Active mode detection; Input design; Set separation; Discrete-time descriptor systems

Domaines: Automatique / Robotique

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, 2019, 107, pp.255-263. ⟨10.1016/j.automatica.2019.05.053⟩. ⟨hal-02430209⟩