Predictor-Based Control of Systems With State Multiplicative Noise

The problem of H∞ state-feedback control of linear continuous-time systems with state multiplicative noise in the presence of input delay is investigated. A predictor-based control is applied, for the first time, to these systems. A new condition for stability is derived in a form of a linear matrix...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2017-02, Vol.62 (2), p.914-920
Main Authors: Gershon, E., Fridman, E., Shaked, U.
Format: Article
Language:English
Subjects:
Continuous time systems
Control systems
Delays
Feedback control
Linear matrix inequalities
Mathematical analysis
Noise
Noise control
Noise prediction
Predictive control
Predictor-control
Process controls
Stability criteria
stochastic <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> H_{\infty}</tex-math> </inline-formula> </named-content> control
Stochastic processes
Stochastic systems
time-delay
Uncertainty
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Summary:The problem of H∞ state-feedback control of linear continuous-time systems with state multiplicative noise in the presence of input delay is investigated. A predictor-based control is applied, for the first time, to these systems. A new condition for stability is derived in a form of a linear matrix inequality. The latter condition is extended to one that guarantees a prescribed L 2 -gain bound for the stochastic system. Solutions are obtained for both constant and time-varying delays. Because of the multiplicative noise, the predictor-based control cannot stabilize the system for arbitrarily large delay. It admits, however, delays that are significantly larger than the delays that can be treated by the corresponding non-predictive state-feedback control. The theoretical results are demonstrated by two examples. The first example shows the advantage of the predictor-based controller and the second one demonstrates the applicability of the theory to process control systems.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2593968