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Robust H2/H∞ control for a class of time-varying nonlinear stochastic systems with state- and control-dependent noises

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  • Ming Gao
  • Zhengmao Zhu
  • Yichun Niu

Abstract

This paper deals with the problem of robust $H_2/H_\infty $H2/H∞ control for a class of discrete time-varying nonlinear stochastic systems with state- and control-dependent noises (also called $(x,u) $(x,u)-dependent noises). In the addressed system, all system parameters are allowed to be time-varying, parameter uncertainties are supposed to be norm-bounded, and nonlinearities are assumed to satisfy the sector-bounded condition. A robust stochastic bounded real lemma is established for the uncontrolled system by means of the Riccati difference equation (RDE). Moreover, a necessary and sufficient condition is presented for the existence of finite-horizon robust $H_2/H_\infty $H2/H∞ control by virtue of the solvability of coupled RDEs, and an iterative algorithm is designed to solve these RDEs. Finally, a numerical example is utilised to illustrate the effectiveness of the derived results.

Suggested Citation

  • Ming Gao & Zhengmao Zhu & Yichun Niu, 2020. "Robust H2/H∞ control for a class of time-varying nonlinear stochastic systems with state- and control-dependent noises," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(7), pages 1218-1228, May.
    • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:7:p:1218-1228
    DOI: 10.1080/00207721.2020.1755742
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