### Abstract

This paper proposes a new tool for quantized nonlinear control design of dynamic systems transformable into the dynamically perturbed strict-feedback form. To address the technical challenges arising from measurement and actuator quantization, a new approach based on set-valued maps is developed to transform the closed-loop quantized system into a large-scale system composed of input-to-state stable (ISS) subsystems. For each ISS subsystem, the inputs consist of quantization errors and interacting states, and moreover, the ISS gains can be assigned arbitrarily. Then, the recently developed cyclic-small-gain theorem is employed to guarantee input-to-state stability with respect to quantization errors and to construct an ISS-Lyapunov function for the closed-loop quantized system. Interestingly, it is shown that, under some realistic assumptions, any n-dimensional dynamically perturbed strict-feedback nonlinear system can be globally practically stabilized by a quantized control law using 2n three-level dynamic quantizers.

Original language | English (US) |
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Pages (from-to) | 75-110 |

Number of pages | 36 |

Journal | Mathematics of Control, Signals, and Systems |

Volume | 24 |

Issue number | 1-2 |

DOIs | |

State | Published - Apr 2012 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Signal Processing
- Applied Mathematics
- Control and Optimization

### Cite this

*Mathematics of Control, Signals, and Systems*,

*24*(1-2), 75-110. https://doi.org/10.1007/s00498-012-0079-x

**Quantized stabilization of strict-feedback nonlinear systems based on ISS cyclic-small-gain theorem.** / Liu, Tengfei; Jiang, Zhong-Ping; Hill, David J.

Research output: Contribution to journal › Article

*Mathematics of Control, Signals, and Systems*, vol. 24, no. 1-2, pp. 75-110. https://doi.org/10.1007/s00498-012-0079-x

}

TY - JOUR

T1 - Quantized stabilization of strict-feedback nonlinear systems based on ISS cyclic-small-gain theorem

AU - Liu, Tengfei

AU - Jiang, Zhong-Ping

AU - Hill, David J.

PY - 2012/4

Y1 - 2012/4

N2 - This paper proposes a new tool for quantized nonlinear control design of dynamic systems transformable into the dynamically perturbed strict-feedback form. To address the technical challenges arising from measurement and actuator quantization, a new approach based on set-valued maps is developed to transform the closed-loop quantized system into a large-scale system composed of input-to-state stable (ISS) subsystems. For each ISS subsystem, the inputs consist of quantization errors and interacting states, and moreover, the ISS gains can be assigned arbitrarily. Then, the recently developed cyclic-small-gain theorem is employed to guarantee input-to-state stability with respect to quantization errors and to construct an ISS-Lyapunov function for the closed-loop quantized system. Interestingly, it is shown that, under some realistic assumptions, any n-dimensional dynamically perturbed strict-feedback nonlinear system can be globally practically stabilized by a quantized control law using 2n three-level dynamic quantizers.

AB - This paper proposes a new tool for quantized nonlinear control design of dynamic systems transformable into the dynamically perturbed strict-feedback form. To address the technical challenges arising from measurement and actuator quantization, a new approach based on set-valued maps is developed to transform the closed-loop quantized system into a large-scale system composed of input-to-state stable (ISS) subsystems. For each ISS subsystem, the inputs consist of quantization errors and interacting states, and moreover, the ISS gains can be assigned arbitrarily. Then, the recently developed cyclic-small-gain theorem is employed to guarantee input-to-state stability with respect to quantization errors and to construct an ISS-Lyapunov function for the closed-loop quantized system. Interestingly, it is shown that, under some realistic assumptions, any n-dimensional dynamically perturbed strict-feedback nonlinear system can be globally practically stabilized by a quantized control law using 2n three-level dynamic quantizers.

UR - http://www.scopus.com/inward/record.url?scp=84859103613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859103613&partnerID=8YFLogxK

U2 - 10.1007/s00498-012-0079-x

DO - 10.1007/s00498-012-0079-x

M3 - Article

VL - 24

SP - 75

EP - 110

JO - Mathematics of Control, Signals, and Systems

JF - Mathematics of Control, Signals, and Systems

SN - 0932-4194

IS - 1-2

ER -