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Minimal Perturbations for Zero Controllability of Discrete-Time Linear Systems: Complexity Analysis.
- Source :
-
IEEE Transactions on Automatic Control . Mar2021, Vol. 66 Issue 3, p1391-1398. 8p. - Publication Year :
- 2021
-
Abstract
- This article deals with computational complexity of various problems related to the zero controllability of a discrete-time linear time-invariant system, assuming that purely structural conditions at the level of the connections between the system states (i.e., state-connections) and the connections from the inputs to the states (i.e., input-connections) are known. Given a generically zero controllable system, we consider the following problems: i) find a minimal set of input-connections whose removal makes the resulting system not generic zero controllability; ii) identify a minimal cost set of input-connections that must be retained from the given set of input-connections while preserving generic zero controllability property; and iii) given a not generically zero controllable system, find a smallest set of state-connections whose removal makes the resulting system generically zero controllable. Problem i) is polynomially solvable. Problems ii) and iii) are NP-hard and approximation results are provided for them. The results of i) and iii) provide clues to analyze the fragility and hardness involved in modifying a system structure. Problem ii) is useful to ensure an accurate discrete-time linear approximation of a large-scale system by maintaining generic zero controllability of the linear system. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189286
- Volume :
- 66
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Automatic Control
- Publication Type :
- Periodical
- Accession number :
- 148970718
- Full Text :
- https://doi.org/10.1109/TAC.2020.2995185