The paper deals with the g2-stability analysis of multi-input-multi-output(MIMO)systems,governed by integral equations,with a matrix of periodic/aperiodic time-varying gains and a vector of monotone,non-monotone and q...The paper deals with the g2-stability analysis of multi-input-multi-output(MIMO)systems,governed by integral equations,with a matrix of periodic/aperiodic time-varying gains and a vector of monotone,non-monotone and quasi-monotone nonlin-earities.For nonlinear MIMO systems that are described by differential equations,most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates.In contrast,a non-Lyapunov framework is employed here to derive new and more general g2-stability conditions in the frequency domain.These conditions have the following features:i)They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block,ii)For certain cases of the periodic time-varying gain,they contain,depending on the multiplier function chosen,no restrictions on the normalized rate of variation of the time-varying gain,but,for other periodic/aperiodic time-varying gains,they do.Overall,even when specialized to periodic-coefficient linear and nonlinear MIMO systems,the stability conditions are distinct from and less restrictive than recent results in the literature.No comparable results exist in the literature for aperiodic time-varying gains.Furthermore,some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented.Examples are given to illustrate a few of the stability theorems.展开更多
New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F...New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.展开更多
Background:Epidemiological studies have confirmed that longer exposure to insecticides like cypermethrin(CYP)significantly increases the risk of male reproductive toxicity.Crocus sativus L.has been recognized due to i...Background:Epidemiological studies have confirmed that longer exposure to insecticides like cypermethrin(CYP)significantly increases the risk of male reproductive toxicity.Crocus sativus L.has been recognized due to its therapeutic properties,but its exact role and molecular mechanisms in treatment of reproductive dysfunction remain unclear.Methods:During this study,36 rats were randomly divided into six groups(n=6):control,CYP-induced(60 mg/kg),standard(leuprolide 3 mg/kg)and three treatment groups receiving aqueous,ethanolic,and oil extracts(50 mg/kg or 20 mL/kg)for post-toxicity induction.Results:The finding represented that exposure of CYP significantly increased oxidative stress,disrupted testicular architecture,and markedly reduced testosterone levels(P<0.05).Importantly,Crocus sativus L.treatment alleviated these changes by increasing the expression of Nrf2(nuclear factor erythroid 2-related factor 2),restoring the activity of antioxidant enzymes,and enhancing testicular histomorphology.Surprisingly,molecular docking established a high binding affinity of Crocus sativus L.phytoconstituents such as gallic acid,cinnamic acid and quercetin to the Nrf2-Keap1 complex.It is worth noting that,Crocus sativus L.exhibited a high level of protection against reproductive toxicity caused by CYP in male rats,which was mediated by the activation of Nrf2 pathway,reduction of oxidative damage,and favorable ADMET characteristics.Conclusion:Notably,this research provides a more valid,safe,and effective method of developing new drugs for reproductive disorders,however,further investigation is needed to support the research findings and implement it in clinical practice.展开更多
文摘The paper deals with the g2-stability analysis of multi-input-multi-output(MIMO)systems,governed by integral equations,with a matrix of periodic/aperiodic time-varying gains and a vector of monotone,non-monotone and quasi-monotone nonlin-earities.For nonlinear MIMO systems that are described by differential equations,most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates.In contrast,a non-Lyapunov framework is employed here to derive new and more general g2-stability conditions in the frequency domain.These conditions have the following features:i)They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block,ii)For certain cases of the periodic time-varying gain,they contain,depending on the multiplier function chosen,no restrictions on the normalized rate of variation of the time-varying gain,but,for other periodic/aperiodic time-varying gains,they do.Overall,even when specialized to periodic-coefficient linear and nonlinear MIMO systems,the stability conditions are distinct from and less restrictive than recent results in the literature.No comparable results exist in the literature for aperiodic time-varying gains.Furthermore,some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented.Examples are given to illustrate a few of the stability theorems.
文摘New conditions are derived for the l2-stability of time-varying linear and nonlinear discrete-time multiple-input multipleoutput （MIMO） systems, having a linear time time-invariant block with the transfer function F（z）, in negative feedback with a matrix of periodic/aperiodic gains A（k）, k = 0,1, 2,... and a vector of certain classes of non-monotone/monotone nonlinearities φp（-）, without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features： i） They involve the positive definiteness of the real part （as evaluated on ｜z｜ = 1） of the product of Г （z） and a matrix multiplier function of z. ii） For periodic A（k）, one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A（k）, but for aperiodic A（k）, which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of （A（k ＋ 1）,A（k））, k = 1, 2 iii） They are distinct from and less restrictive than recent results in the literature.
文摘Background:Epidemiological studies have confirmed that longer exposure to insecticides like cypermethrin(CYP)significantly increases the risk of male reproductive toxicity.Crocus sativus L.has been recognized due to its therapeutic properties,but its exact role and molecular mechanisms in treatment of reproductive dysfunction remain unclear.Methods:During this study,36 rats were randomly divided into six groups(n=6):control,CYP-induced(60 mg/kg),standard(leuprolide 3 mg/kg)and three treatment groups receiving aqueous,ethanolic,and oil extracts(50 mg/kg or 20 mL/kg)for post-toxicity induction.Results:The finding represented that exposure of CYP significantly increased oxidative stress,disrupted testicular architecture,and markedly reduced testosterone levels(P<0.05).Importantly,Crocus sativus L.treatment alleviated these changes by increasing the expression of Nrf2(nuclear factor erythroid 2-related factor 2),restoring the activity of antioxidant enzymes,and enhancing testicular histomorphology.Surprisingly,molecular docking established a high binding affinity of Crocus sativus L.phytoconstituents such as gallic acid,cinnamic acid and quercetin to the Nrf2-Keap1 complex.It is worth noting that,Crocus sativus L.exhibited a high level of protection against reproductive toxicity caused by CYP in male rats,which was mediated by the activation of Nrf2 pathway,reduction of oxidative damage,and favorable ADMET characteristics.Conclusion:Notably,this research provides a more valid,safe,and effective method of developing new drugs for reproductive disorders,however,further investigation is needed to support the research findings and implement it in clinical practice.
