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Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems. (English) Zbl 1453.93216

Summary: This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

MSC:

93D40 Finite-time stability
93D25 Input-output approaches in control theory
93E15 Stochastic stability in control theory
93B53 Observers
93B52 Feedback control
93C10 Nonlinear systems in control theory
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