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Closed-loop stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm

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Abstract

Reduced multiple-model control design as an alternative approach to control complex nonlinear systems could bring about the simplicity in system analysis, control design, and implementation and could guarantee the local stability using two tools: gap metric and stability margin. This is while a study on closed-loop stability of nonlinear systems remains a contentious issue which is left to be solved. We introduced a stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm, whereby the closed-loop stability will be met driven via Lyapunov approach. The stabilizing strategy is applied to design a reduced multiple-model control using linear matrix inequality. The global stability could be guaranteed via such a valuable approach. This is illustrated on a complex nonlinear system, which is modeled around two different operating points to describe its strong nonlinearities. The closed-loop stability properties are also illustrated via computer simulations.

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Abbreviations

BG:

Blood glucose

GDD:

Glucose-dependent desired

HOLLM:

High order local linear model

HOM:

High order model

HOMB:

High order model bank

HONLM:

High order nominal linear models

HVAC:

Heating, ventilation, and air conditioning

IAE:

Integral absolute error

ISE:

Integral square error

ITAE:

Integral time absolute error

ITSE:

Integral time square error

LMI:

Linear matrix inequalities

MM:

Multiple-model

MS:

Model simplicity

NM:

Nonlinearity measure

OR:

Order reduction

RMM:

Reduced multiple-model

ROM:

Reduced order model

RONLM:

Reduced order nominal linear model

T1DM:

Type 1 diabetes mellitus

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Authors and Affiliations

  1. Department of Mechanical, Electrical, and Computer Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Pouya Rikhtehgar

  2. Advanced Control Systems Lab, Electrical Engineering, Sharif University of Technology, Tehran, Iran

    Mohammad Haeri

Authors
  1. Pouya Rikhtehgar
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  2. Mohammad Haeri
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by PR and MH. The first draft of the manuscript was written by PR and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Mohammad Haeri.

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Rikhtehgar, P., Haeri, M. Closed-loop stability analysis of a linear matrix inequalities based reduced multiple-model control algorithm. Int. J. Dynam. Control (2023). https://doi.org/10.1007/s40435-023-01354-8

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  • DOI: https://doi.org/10.1007/s40435-023-01354-8

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