共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we are concerned with admissible trajectories x(·) of infinite-dimensional linear systems, defined on an interval [0, t1] and such that x(0)−x(t1) is small. We show that these trajectories satisfy certain geometric properties. 相似文献
2.
Richard Rebarber 《Systems & Control Letters》1990,14(4)
Let A be a generator of a strongly continuous semigroup of operators, and assume that C and H are operators such that A + CH generates a strongly continuous semigroup SH(t) on X. Let λ0 be a real number in the resolvent set of A, and let ε [−1, 1]. Then there are some fairly unrestrictive conditions under which A+(λ0 − A)CH(λ0 − A)− also generates a strongly continuous semigroup SK(t) on X which has the same exponential growth rate as SH(t). Given an input operator B, we can use this to identify a class of feedback perturbations K such that A + BK generates a strongly continuous semigroup. We can also use this result to identify classes of feedbacks which can and cannot uniformly stabilize a system. For example, we show that if the control on a cantilever beam in the state space H02[0, 1] × L2[0, 1] is a moment force on the free end, then we cannot stabilize the beam with an A−1/2-bounded feedback, but we can find an A−1/4-bounded feedback, for any > 0, which does stabilize the beam. 相似文献
3.
Xuerong Mao 《Systems & Control Letters》1995,26(4)
The aim of this paper is to investigate the exponential stability in mean square for a neutral stochastic differential functional equation of the form d[x(t) − G(xt)] = [f(t,x(t)) + g(t, xt)]dt + σ(t, xt)dw(t), where xt = {x(t + s): − τ s 0}, with τ > 0, is the past history of the solution. Several interesting examples are a given for illustration. 相似文献
4.
In this paper the quasilinear heat equation with the nonlinear boundary condition is studied. The blow-up rate and existence of a self-similar solution are obtained. It is proved that the rescaled function
v(y,t)=(T−t)1/(2p+α−2)u((T−t)(p−1)/(2p+α−2)y,t),