Asynchronous ℋ control for two-dimensional hidden Markovian jump systems with partly known mode observation conditional probabilities

Jin Zhu, Chaoxiang Li, Geir E. Dullerud

Research output: Contribution to journalArticlepeer-review

Abstract

This study focuses on the asynchronous (Formula presented.) control problem for two-dimensional discrete-time hidden Markovian jump systems where the mode observation conditional probability matrix is partly known. Considering the original system modes are invisible, the observed modes emitted from an observer serve as an alternative for stability analysis and controller design where a mode observation conditional probability matrix is constructed to characterize the emission between system modes and observed modes. Specially, only partly known information of the mode observation conditional probability matrix is accessible. With the introduction of the free-connection weighting matrices, the asymptotic mean square stability criterion is firstly derived based on Lyapunov method. This introduction provides a further degree of relaxation and less conservatism is therefore achieved. Secondly, we present synthesis conditions for asynchronous (Formula presented.) state feedback controller design given in terms of a set of interconnected linear matrix inequalities. Moreover, cluster concept based on the partitions of observed modes is adopted which helps to decrease the number of controllers and simplify the design complexity. A numerical example, regarding the cases with and without clustering of the observed modes, is presented to illustrate the effectiveness of the proposed method.

Original languageEnglish (US)
Pages (from-to)3344-3364
Number of pages21
JournalInternational Journal of Robust and Nonlinear Control
Volume30
Issue number8
DOIs
StatePublished - May 25 2020

Keywords

  • asynchronous control
  • free-connection weighting matrices
  • partly known mode observation conditional probability matrix
  • two-dimensional hidden Markovian jump systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Chemical Engineering(all)
  • Biomedical Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering

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