H control for continuous-time Markov jump nonlinear systems with piecewise-affine approximation

Yanzheng Zhu, Nuo Xu, Xinkai Chen, Wei Xing Zheng

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

This paper investigates the problem of stability, H performance analysis, and H control for continuous-time Markov jump nonlinear systems, where the nonlinear subsystems are approximated by the piecewise-affine technique. The proposed Markov jump piecewise-affine systems contain different modes and regions, both of which are determined by Markov chains and piecewise-affine partitions, respectively. A new admissible adjacent region switching paths (AARSPs) algorithm is proposed for the first time in the continuous-time domain to decrease the conservatism of the complete adjacent region switching paths (CARSPs) algorithm. This new algorithm optimizes the path selection conditions of the next instantaneous time region switching in the CARSPs algorithm, and effectively reduces the computational complexity and the conservatism of the CARSPs algorithm. Furthermore, a state-feedback piecewise-linear controller is designed by means of the ellipsoidal outer approximation estimation method, such that the corresponding closed-loop system is stochastically stable and has a guaranteed H performance index. Finally, the effectiveness and practicability of both the AARSPs algorithm and the piecewise-linear control strategy are fully demonstrated via two illustrative examples including a class of tunnel diode circuit systems.

Original languageEnglish
Article number110300
JournalAutomatica
Volume141
DOIs
Publication statusPublished - 2022 Jul

Keywords

  • Admissible adjacent region switching paths
  • H control
  • Markov jump piecewise-affine systems
  • Piecewise-linear controller
  • Tunnel diode circuit system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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