State-feedback H∞ control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise

Huiping Li, Yang Shi

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

This article focuses on the state-feedback H∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton-Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback H∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback H∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Original languageEnglish
Pages (from-to)1515-1531
Number of pages17
JournalInternational Journal of Control
Volume85
Issue number10
DOIs
StatePublished - 1 Oct 2012
Externally publishedYes

Keywords

  • delay-dependent conditions
  • delay-independent conditions
  • Hamilton-Jacobi-inequality
  • Lyapunov-Krasovskii functional
  • state-feedback H∞ control
  • stochastic nonlinear system
  • time-varying delays

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