Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 85, Issue 10, Pages 1515-1531Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2012.691181
Keywords
stochastic nonlinear system; state-feedback H-infinity control; Hamilton-Jacobi-inequality; time-varying delays; Lyapunov-Krasovskii functional; delay-independent conditions; delay-dependent conditions
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Funding
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Canada Foundation for Innovation (CFI)
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This article focuses on the state-feedback H-infinity 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-infinity 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-infinity controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.
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