A new decentralised controller design method for a class of strongly interconnected systems

Zhisheng Duan, Zhong-Ping Jiang, Lin Huang

Research output: Contribution to journalArticle

Abstract

In this paper, two interconnected structures are first discussed, under which some closed-loop subsystems must be unstable to make the whole interconnected system stable, which can be viewed as a kind of strongly interconnected systems. Then, comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown. A new approach for the design of decentralised controllers is presented by determining the Lyapunov function structure previously, which allows the existence of unstable subsystems. By fully utilising the orthogonal space information of input matrix, some new understandings are presented for the construction of Lyapunov matrix. This new method can deal with decentralised state feedback, static output feedback and dynamic output feedback controllers in a unified framework. Furthermore, in order to reduce the design conservativeness and deal with robustness, a new robust decentralised controller design method is given by combining with the parameter-dependent Lyapunov function method. Some basic rules are provided for the choice of initial variables in Lyapunov matrix or new introduced slack matrices. As byproducts, some linear matrix inequality based sufficient conditions are established for centralised static output feedback stabilisation. Effects of unstable subsystems in nonlinear Lur'e systems are further discussed. The corresponding decentralised controller design method is presented for absolute stability. The examples illustrate that the new method is significantly effective.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalInternational Journal of Control
DOIs
StateAccepted/In press - May 1 2016

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Large scale systems
Controllers
Lyapunov functions
Feedback
Linear matrix inequalities
State feedback
Robustness (control systems)
Byproducts
Stabilization

Keywords

  • absolute stability
  • Decentralised control
  • large gain coupling, strict positive realness (SPR)
  • unstable subsystems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications

Cite this

A new decentralised controller design method for a class of strongly interconnected systems. / Duan, Zhisheng; Jiang, Zhong-Ping; Huang, Lin.

In: International Journal of Control, 01.05.2016, p. 1-17.

Research output: Contribution to journalArticle

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