Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems

Ye Wang (1) , Sorin Olaru (2) , Giorgio Valmorbida (2) , Vicenç Puig (1) , Gabriela Cembrano (1)

1 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]
2 L2S - Laboratoire des signaux et systèmes

In this paper, the computation of robust invariant sets for discrete-time uncertain descriptor systems are investigated. The studied descriptor systems are assumed to be regular and stable subject to unknown but bounded disturbances. The robust invariant sets of both causal and non-causal descriptor systems are studied. It is recalled that a descriptor system can be transformed into an equivalent system by using a suitable linear coordinate transformation. Transformations for causal and non-causal descriptor systems are used in the characterization of the effect of the disturbances. For causal descriptor systems, two robust positively invariant (RPI) sets are computed separately. For non-causal descriptor systems, an RPI set and a robust negatively invariant (RNI) set can be found. As a result, the general RPI set of a descriptor system can be obtained from a linear projection image of these two sets. Besides, active mode detection method is proposed based on set invariance theory.

Domaines: Automatique / Robotique

Ye Wang, Sorin Olaru, Giorgio Valmorbida, Vicenç Puig, Gabriela Cembrano. Robust invariant sets and active mode detection for discrete-time uncertain descriptor systems. 56th IEEE Conference on Decision and Control (CDC 2017), Dec 2017, Melbourne, Australia. ⟨10.1109/CDC.2017.8264511⟩. ⟨hal-01710292⟩