Nonlinear stochastic passivity, feedback equivalence and global stabilization. (English) Zbl 1273.93170
Summary: This paper addresses several important issues including stochastic passivity, feedback equivalence and global stabilization for a class of nonlinear stochastic systems. Based on a nonlinear stochastic Kalman-Yacubovitch-Popov (KYP) lemma, we investigate the relationship between a stochastic passive system and the corresponding zero-output system. Different from the deterministic case, it is shown for the first time that feedback equivalence to a stochastic passive system requires a strong minimum-phase condition, not the minimum-phase one. Following the stochastic passivity theory, global stabilization results are established for a class of nonlinear stochastic systems with relative degree \(1\leq r<n\). An example is presented to illustrate the effectiveness of our results.
MSC:
| 93E15 | Stochastic stability in control theory |
| 93C10 | Nonlinear systems in control theory |
| 93E03 | Stochastic systems in control theory (general) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
stochastic systems; nonlinear systems; passive systems; stability in probability; nonlinear stochastic Kalman-Yacubovitch-Popov (KYP) lemmaReferences:
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