This paper deals with the output feedback H ∞ control problem for a class of nonlinear stochastic systems.Based on the latest developed theory of stochastic dissipation,a notable result about the nonlinear H ∞ output feedback control of deterministic system is generalized to the stochastic case.Finally,in the cases of state feedback and output feedback,two families of controllers are provided respectively.
In this paper,we develop a new mathematical model for the mammalian circadian clock,which incorporates both transcriptional/translational feedback loops (TTFLs) and a cAMP-mediated feedback loop.The model shows that TTFLs and cAMP signalling cooperatively drive the circadian rhythms.It reproduces typical experimental observations with qualitative similarities,e.g.circadian oscillations in constant darkness and entrainment to light-dark cycles.In addition,it can explain the phenotypes of cAMP-mutant and Rev-erbα-/-mutant mice,and help us make an experimentally-testable prediction:oscillations may be rescued when arrhythmic mice with constitutively low concentrations of cAMP are crossed with Rev-erbα-/mutant mice.The model enhances our understanding of the mammalian circadian clockwork from the viewpoint of the entire cell.
