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 noncausal 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.

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.…”

Fault-Tolerant Control Based on Virtual Actuator and Sensor for Discrete-Time Descriptor Systems

“…On the other hand, active FTC reacts to faults by performing some reconfiguration action based on online information coming from a fault diagnosis module [14]. Recently, a few works have considered fault diagnosis [15], [16] and FTC [17]- [19] for descriptor systems. However, these techniques require an online modification of the controller/observer so that in presence of an already designed and operating control system, fault tolerance can be enforced only by means of redesigning from the scratch its components.…”

“…withP as in (17), and φ 1 , φ 2 and φ 3 as in (14). Proof: Consider the matrixÊ ⊥ = E ⊥ 0 , which is of full row rank and satisfiesÊ ⊥Ê = 0 withÊ defined as in (16). From (18), we have that…”

Set-membership estimation for linear time-varying descriptor systems

“…However, only few results study setmembership estimation for descriptor systems. Wang, Puig & Cembrano (2018a) and Wang, Olaru, Valmorbida, Puig & Cembrano (2019a) studied set-membership estimation methods for descriptor systems based on zonotopes. However, Wang et al (2018a) and Wang et al (2019a) only considered time-invariant systems.…”