Output Controllability of a Linear Dynamical System with Sparse Controls

Journal article (2023)

Authors

G. Joseph Signal Processing Systems - EEMCS
Research Group
Signal Processing Systems (EEMCS) (TU Delft)
Copyright: © 2023 G. Joseph
DOI
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https://doi.org/10.1109/TCNS.2022.3188484
Sparsity Controllability Linear dynamical systems Time-varying support Discrete-time system Output controllability Kalman rank test Optimal sparse control General linear systems Minimal input
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Microelectronics

Research Group

Signal Processing Systems

Abstract

In this article, we study the conditions to be satisfied by a discrete-time linear system to ensure output controllability using sparse control inputs. A set of necessary and sufficient conditions can be directly obtained by extending the Kalman rank test for output controllability. However, the verification of these conditions is computationally heavy due to their combinatorial nature. Therefore, we derive noncombinatorial conditions for output sparse controllability that can be verified with polynomial time complexity. Our results also provide bounds on the minimum sparsity level required to ensure output controllability of the system. This additional insight is useful for designing sparse control input that drives the system to any desired output.