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
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
为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现...为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L_(2)灵敏度表达式,并进行稀疏化校准,将L_(2)灵敏度最小化问题转换为凸函数求最值问题,求导得到L_(2)灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.展开更多
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.
文摘为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L_(2)灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L_(2)灵敏度表达式,并进行稀疏化校准,将L_(2)灵敏度最小化问题转换为凸函数求最值问题,求导得到L_(2)灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.
