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

Tengfei Liu, Zhong-Ping Jiang, David J. Hill

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)75-110
Number of pages36
JournalMathematics of Control, Signals, and Systems
Volume24
Issue number1-2
DOIs
StatePublished - Apr 2012

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Small Gain Theorem
Feedback Systems
Closed loop systems
Nonlinear systems
Stabilization
Nonlinear Systems
Feedback
Quantization
Lyapunov functions
Closed-loop
Large scale systems
Dynamical systems
Subsystem
Actuators
Set-valued Map
Nonlinear Control
Large-scale Systems
Control Design
Lyapunov Function
Dynamic Systems

ASJC Scopus subject areas

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

Cite this

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

In: Mathematics of Control, Signals, and Systems, Vol. 24, No. 1-2, 04.2012, p. 75-110.

Research output: Contribution to journalArticle

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