Advances in Stabilization of Hybrid Stochastic Differential Equations by Delay Feedback Control
Junhao Hu, Wei Liu, Feiqi Deng, Xuerong Mao
Abstract
A novel approach for designing the feedback control based on past states is proposed for hybrid stochastic differential equations (SDEs). This new theorem builds up the connection between the delay feedback control and the control function without delay terms, which enables one to construct the delay feedback control using the existing results on stabilities of hybrid SDEs. Methods for finding the upper bound of the length of the time delay are also investigated. Numerical simulations are presented to demonstrate the new theorem.
Topics & Concepts
MathematicsDelay differential equationControl theory (sociology)Feedback controlStochastic differential equationConnection (principal bundle)Control (management)Upper and lower boundsConstruct (python library)Function (biology)Differential (mechanical device)Applied mathematicsDifferential equationComputer scienceMathematical analysisControl engineeringEvolutionary biologyGeometryArtificial intelligenceBiologyEngineeringProgramming languageAerospace engineeringStability and Controllability of Differential EquationsStochastic processes and financial applicationsNeural Networks Stability and Synchronization