A matrix theoretic characterization of the strongly reachable subspace
Imrul Qais, Chayan Bhawal, and Debasattam Pal
TL;DR
This paper introduces new matrix-based characterizations of key subspaces in state-space systems, linking strongly reachable subspaces to impulsive inputs and providing formulas for their dimensions.
Contribution
It offers novel closed-form representations of weakly unobservable and strongly reachable subspaces, enhancing understanding and computation in control theory.
Findings
Strongly reachable subspace relates to admissible impulsive inputs.
Closed-form formulas for subspace dimensions from transfer matrix.
New characterizations improve analysis of state-space systems.
Abstract
In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said subspaces. In this process, we establish that the strongly reachable subspace is intimately related to the space of admissible impulsive inputs. We also show how to calculate the dimensions of these subspaces from the transfer matrix of the system.
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Taxonomy
TopicsControl and Stability of Dynamical Systems · Stability and Control of Uncertain Systems · Control Systems and Identification