Using artificial delays for prescribed/fixed-time static output feedback control of linear systems

Abstract

In this paper, we address the prescribed/fixed-time control problem for linear time-invariant systems with relative degree r≥ 2 using delayed time-varying static output feedback. In addition to controllability and observability, we assume that a truncated observability matrix is nonsingular. Within the act-and-wait control framework, two types of artificial delays are introduced into the output feedback: one to realize static output feedback and the other to achieve prescribed/fixed-time control. By constructing smooth periodic delayed output feedback controllers, we achieve prescribed-time input-to-state stability (ISS) with respect to matched disturbances and measurement noise. Next, we consider systems with measurement delays. Note that existing predictor methods are not applicable to static output feedback delay compensation. We propose delayed controllers that achieve fixed-time stability in the presence of large known slowly-varying delays (with delay derivatives less than one) and even in the presence of large unknown constant delays for systems with nilpotent matrices. Moreover, we present a design for the case of discrete-time periodic measurements with a small sampling period. When the system reduces to a chain of integrators, prescribed/fixed-time convergence can be achieved with arbitrarily large artificial delays introduced by static output feedback avoiding high gain and managing with large known slowly-varying or sawtooth delays (corresponding to discrete-time measurements) or unknown constant delays. In the case of unknown constant delays, this leads to a low-gain controller that may efficiently attenuate measurement noise. Numerical examples verify the effectiveness of the proposed method.

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BibTeX RIS

BibTeX

@misc{zhang2026using,
  title = {{Using artificial delays for prescribed/fixed-time static output feedback control of linear systems}},
  author = {Kang-Kang Zhang and Emilia Fridman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33878},
  eprint = {2610.33878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33878},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Using artificial delays for prescribed/fixed-time static output feedback control of linear systems
AU  - Kang-Kang Zhang
AU  - Emilia Fridman
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33878
UR  - https://arxiv.org/abs/2610.33878
AB  - In this paper, we address the prescribed/fixed-time control problem for linear time-invariant systems with relative degree r≥ 2 using delayed time-varying static output feedback. In addition to controllability and observability, we assume that a truncated observability matrix is nonsingular. Within the act-and-wait control framework, two types of artificial delays are introduced into the output feedback: one to realize static output feedback and the other to achieve prescribed/fixed-time control. By constructing smooth periodic delayed output feedback controllers, we achieve prescribed-time input-to-state stability (ISS) with respect to matched disturbances and measurement noise. Next, we consider systems with measurement delays. Note that existing predictor methods are not applicable to static output feedback delay compensation. We propose delayed controllers that achieve fixed-time stability in the presence of large known slowly-varying delays (with delay derivatives less than one) and even in the presence of large unknown constant delays for systems with nilpotent matrices. Moreover, we present a design for the case of discrete-time periodic measurements with a small sampling period. When the system reduces to a chain of integrators, prescribed/fixed-time convergence can be achieved with arbitrarily large artificial delays introduced by static output feedback avoiding high gain and managing with large known slowly-varying or sawtooth delays (corresponding to discrete-time measurements) or unknown constant delays. In the case of unknown constant delays, this leads to a low-gain controller that may efficiently attenuate measurement noise. Numerical examples verify the effectiveness of the proposed method.
ER  -

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