The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlineariti...The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.展开更多
The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained ...The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained the functions of the jump ra-nge,and examined the effects of the A MB's parameters.展开更多
In this paper,we use the ordinary differential equation theory of Banach spaces and minimax theory,and in particular,the relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping n...In this paper,we use the ordinary differential equation theory of Banach spaces and minimax theory,and in particular,the relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and get new multiple solutions and sign- changing solutions theorems,at last we get up to six nontrivial solutions.展开更多
We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions.
In this paper,Fucik spectrum,ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and so...In this paper,Fucik spectrum,ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and some new results on the existence of nontrivial solutions,multiple solutions and sign-changing solutions are obtained.In one case seven nontrivial solutions are got.The techniques have independent interest.展开更多
In this paper, we consider the system where A(λ) is a linear transformation on Rn for each λ, α (λ,x) is an operator from R × Rn to Rn and λ is a real parameter. We examine large periodic solutions and drop ...In this paper, we consider the system where A(λ) is a linear transformation on Rn for each λ, α (λ,x) is an operator from R × Rn to Rn and λ is a real parameter. We examine large periodic solutions and drop the assumption of continuity of a(λ,x) near the origin. We consider what happens if a pair of eigenvalues of the linear part of the right hand side in (0. 1) crosses the imaginary axis for large where denotes the norm in Rn.展开更多
In the present paper, the author studies the existence of sign-changing solutions for nonlinear elliptic equations, which have jumping nonlinearities, and may or may not be resonant with respect to Fucik spectrum, via...In the present paper, the author studies the existence of sign-changing solutions for nonlinear elliptic equations, which have jumping nonlinearities, and may or may not be resonant with respect to Fucik spectrum, via linking methods under Cerami condition.展开更多
基金supported partly by the National Natural Science Foundation of China(60574001)the Program for New Century Excellent Talents in University(050485)the Program for Innovative Research Team of Jiangnan University.
文摘The exponential passive filtering problem for a class of nonlinear Markov jump systems with uncertainties and time-delays is studied. The uncertain parameters are assumed unknown but norm bounded, and the nonlinearities satisfy the quadratic condition. Based on the passive filtering theory, the sufficient condition for the existence of the mode-dependent passive filter is given by analyzing the reconstructed observer system. By using the appropriate Lyapnnov-Krasovskii function and applying linear matrix inequalities, the design scheme of the passive filter is derived and described as an optimization one. The presented exponential passive filter makes the error dynamic systems exponentially stochastically stable for all the admissible uncertainties, time-delays and nonlinearities, has the better abilities of state tracking and satisfies the given passive norm index. Simulation results demonstrate the validity of the proposed approach.
文摘The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained the functions of the jump ra-nge,and examined the effects of the A MB's parameters.
基金Research supported by the National Natural Science Foundation of China and Postdoctoral Foundation of China
文摘In this paper,we use the ordinary differential equation theory of Banach spaces and minimax theory,and in particular,the relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and get new multiple solutions and sign- changing solutions theorems,at last we get up to six nontrivial solutions.
基金Supported by the Natural Science Foundation of China(10001025)the Natural Science Foundation of Beijing(1022003)the Foundation of Beijing Educational Committee
文摘We provide sufficient conditions for the existence and multiplicity of periodic solutions for Duffing's equations with jumping nonlinearities under resonance conditions.
基金This work was supported by the Australian Research Council and the National Natural Science Foundation of China (Grant No. 2178200) the Foundation of State Education Commission for Returned Overseas Scholars.
文摘In this paper,Fucik spectrum,ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity,and some new results on the existence of nontrivial solutions,multiple solutions and sign-changing solutions are obtained.In one case seven nontrivial solutions are got.The techniques have independent interest.
文摘In this paper, we consider the system where A(λ) is a linear transformation on Rn for each λ, α (λ,x) is an operator from R × Rn to Rn and λ is a real parameter. We examine large periodic solutions and drop the assumption of continuity of a(λ,x) near the origin. We consider what happens if a pair of eigenvalues of the linear part of the right hand side in (0. 1) crosses the imaginary axis for large where denotes the norm in Rn.
基金Project supported by the National Natural Science Foundation of China(No.10571123)the Shandong Provincial Natural Science Foundation of China(No.Y2006A04).
文摘In the present paper, the author studies the existence of sign-changing solutions for nonlinear elliptic equations, which have jumping nonlinearities, and may or may not be resonant with respect to Fucik spectrum, via linking methods under Cerami condition.
