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 language | English |
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Pages (from-to) | 1515-1531 |
Number of pages | 17 |
Journal | International Journal of Control |
Volume | 85 |
Issue number | 10 |
DOIs | |
State | Published - 1 Oct 2012 |
Externally published | Yes |
Keywords
- delay-dependent conditions
- delay-independent conditions
- Hamilton-Jacobi-inequality
- Lyapunov-Krasovskii functional
- state-feedback H∞ control
- stochastic nonlinear system
- time-varying delays