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Zbl 1227.93127
Yin, Yanyan; Shi, Peng; Liu, Fei
Gain-scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities. (English)
[J] J. Franklin Inst. 348, No. 4, 685-702 (2011). ISSN 0016-0032; ISSN 1879-2693/e

Summary: This paper studies the problem of continuous gain-scheduled PI tracking control on a class of stochastic nonlinear systems subject to partially known jump probabilities and time-varying delays. First, a gradient linearization procedure is used to construct model-based linear stochastic systems in the vicinity of selected operating states. Next, based on stochastic Lyapunov stabilization analysis, sufficient conditions for the existence of a PI tracking control are established for each linear model in terms of linear matrix inequalities. Finally, a continuous gain-scheduled approach is employed to design continuous nonlinear PI tracking controllers on the entire nonlinear jump system. A simulation example is given to illustrate the effectiveness of the developed design techniques.

MSC 2000:: *93E15 Stochastic stability
93C10 Nonlinear control systems
60J75 Jump processes
93B18 Linearizability of systems

Keywords: PI tracking control; stochastic nonlinear systems; partially known jump probabilities; gradient linearization procedure; stochastic Lyapunov stabilization

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