### Abstract

This paper addresses the stabilization of discrete-time linear systems with random delays, which is a common problem in networked control systems. The delays are assumed to be bounded and longer than a sampling time unit. We apply the act-and-wait control concept to stabilize the system: the controller is on for one sampling period (act) and off for some sampling periods (wait). If the waiting period is longer than the maximum delay in the feedback, then the stability can be described by finite number of eigenvalues. Although the closed-loop stability of the stochastic system with the act-and-wait controller is characterized by the Lyapunov exponent of infinite random matrix products, the dimension of these matrices is finite, which results in a significant reduction of computational complexity. The applicability of this method is demonstrated in a simple example, where we compare deterministic stability with the Lyapunov exponent based results.

Original language | English |
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Title of host publication | Proceedings of the American Control Conference |

Pages | 5440-5443 |

Number of pages | 4 |

Publication status | Published - 2012 |

Event | 2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012 |

### Other

Other | 2012 American Control Conference, ACC 2012 |
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Country | Canada |

City | Montreal, QC |

Period | 6/27/12 → 6/29/12 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the American Control Conference*(pp. 5440-5443). [6315674]

**Act-and-wait control of discrete systems with random delays.** / Ghasemi, Mohammadreza; Zhao, Siming; Insperger, T.; Kalmar-Nagy, Tamas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the American Control Conference.*, 6315674, pp. 5440-5443, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12.

}

TY - GEN

T1 - Act-and-wait control of discrete systems with random delays

AU - Ghasemi, Mohammadreza

AU - Zhao, Siming

AU - Insperger, T.

AU - Kalmar-Nagy, Tamas

PY - 2012

Y1 - 2012

N2 - This paper addresses the stabilization of discrete-time linear systems with random delays, which is a common problem in networked control systems. The delays are assumed to be bounded and longer than a sampling time unit. We apply the act-and-wait control concept to stabilize the system: the controller is on for one sampling period (act) and off for some sampling periods (wait). If the waiting period is longer than the maximum delay in the feedback, then the stability can be described by finite number of eigenvalues. Although the closed-loop stability of the stochastic system with the act-and-wait controller is characterized by the Lyapunov exponent of infinite random matrix products, the dimension of these matrices is finite, which results in a significant reduction of computational complexity. The applicability of this method is demonstrated in a simple example, where we compare deterministic stability with the Lyapunov exponent based results.

AB - This paper addresses the stabilization of discrete-time linear systems with random delays, which is a common problem in networked control systems. The delays are assumed to be bounded and longer than a sampling time unit. We apply the act-and-wait control concept to stabilize the system: the controller is on for one sampling period (act) and off for some sampling periods (wait). If the waiting period is longer than the maximum delay in the feedback, then the stability can be described by finite number of eigenvalues. Although the closed-loop stability of the stochastic system with the act-and-wait controller is characterized by the Lyapunov exponent of infinite random matrix products, the dimension of these matrices is finite, which results in a significant reduction of computational complexity. The applicability of this method is demonstrated in a simple example, where we compare deterministic stability with the Lyapunov exponent based results.

UR - http://www.scopus.com/inward/record.url?scp=84869450773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869450773&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84869450773

SN - 9781457710957

SP - 5440

EP - 5443

BT - Proceedings of the American Control Conference

ER -