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

Abstract

In this paper, the computation of robust invariant sets for discrete-time uncertain descriptor systems is 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. 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.

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

“…• (A general framework for set-invariance characterizations of discrete-time descriptor systems) This framework completes the preliminary results in Wang, Olaru et al (2017). In addition, the convergence time for each RI set and the results of checking the compatible initial states are provided.…”

“…The preliminary results presented in this paper have been reported in Wang, Olaru, Valmorbida, Puig and Cembrano (2017). Additional improvements and new contribution are summarized as follows:…”

Advances in State Estimation, Diagnosis and Control of Complex Systems

“…We use ultimate boundedness of trajectories to obtain set-invariance characterizations for the systems subject to unknown-but-bounded disturbances. The contributions of this chapter have been published and submitted in [141] and [142], respectively. The proposed computation of invariant sets relies on partitioning the state space of descriptor systems considering both causal and non-causal parts.…”