6533b85afe1ef96bd12b8b54
RESEARCH PRODUCT
Stability of stochastic nonlinear systems with state-dependent switching
Zhaojing WuPeng ShiHamid Reza KarimiMingyue Cuisubject
stochastic systemsStability (learning theory)Mathematical proofnonlinear control systemsSet (abstract data type)State-dependent switching; Stochastic systems; Switched systems; Control and Systems Engineering; Computer Science Applications1707 Computer Vision and Pattern Recognition; Electrical and Electronic EngineeringExponential stabilityControl theoryElectrical and Electronic EngineeringSwitched systemsMathematicsLyapunov methodsStochastic systemsSeries (mathematics)Stochastic processApplied MathematicsComputer Science Applications1707 Computer Vision and Pattern Recognitionstate-dependent switchingstabilityComputer Science ApplicationsNonlinear systemControl and Systems EngineeringState dependentswitched systemscontrol system synthesisState-dependent switchingdescription
In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-solution to the underlying problem is constructed and the boundedness criterion is proposed. The significance of this paper is that all the results presented depend on some easily-verified assumptions that are as elegant as those in the deterministic case, and the proofs themselves provide design procedures for switching controls. Refereed/Peer-reviewed
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-08-01 |