Nonsmooth stabilization of a class of Markovian jump stochastic nonlinear systems with parametric and dynamic uncertainties. (English) Zbl 1422.93184
Summary: In this paper, we investigate the finite-time stabilization of Markovian jump stochastic nonlinear (SNL) systems with dynamic uncertainties. Firstly, a proper criterion on finite-time globally asymptotically stability in probability (FGSP) and some useful lemmas are introduced. Then, overcoming the influence of coupled item which determined by Markovian switching, by adding a power integrator technique and induction method, a state-feedback finite-time controller is explicitly constructed. It is proven that, the system state of the closed-loop systems is FGSP. Simulation examples illustrate the effectiveness of our method.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93C10 | Nonlinear systems in control theory |
| 93C41 | Control/observation systems with incomplete information |
| 60J75 | Jump processes (MSC2010) |
| 93D15 | Stabilization of systems by feedback |
| 93C40 | Adaptive control/observation systems |
Keywords:
stochastic nonlinear system; Markovian jump system; finite-time globally asymptotically stable in probability; adaptive controlReferences:
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