Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semi...Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.展开更多
The restriction of KB averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillation u″+ω20u=εkcos ωt-εu3 is obtained by Struble technique. The conclusion about this oscillat...The restriction of KB averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillation u″+ω20u=εkcos ωt-εu3 is obtained by Struble technique. The conclusion about this oscillation derived with other method is discussed. The results show that KB method will break down when a and θ in the zeroth solution of above eqation are not slowly varying functions of time t. The stationary solution of weakly nonlinear oscillation, u″+ω20u=εkcosω(ε)t-εu3 is also analysed.展开更多
基金supported by the National Natural Science Foundation of China(60674018)
文摘Perturbation and robust controllability of the singular distributed parameter control system are discussed via functional analysis and the theory of GE-semigroup in Hilbert space. The perturbation principle of GE-semigroup and the sufficient condition concerning the robust controllability of the singular distributed parameter control system are obtained, in which the controllability for singular distributed parameter control system is not destroyed, if we perturb the equation by small bounded linear operator.
文摘The restriction of KB averaging method is discussed and asymptotic solution of the weakly nonlinear and forced oscillation u″+ω20u=εkcos ωt-εu3 is obtained by Struble technique. The conclusion about this oscillation derived with other method is discussed. The results show that KB method will break down when a and θ in the zeroth solution of above eqation are not slowly varying functions of time t. The stationary solution of weakly nonlinear oscillation, u″+ω20u=εkcosω(ε)t-εu3 is also analysed.
