8,864 research outputs found
Stability Analysis of Integral Delay Systems with Multiple Delays
This note is concerned with stability analysis of integral delay systems with
multiple delays. To study this problem, the well-known Jensen inequality is
generalized to the case of multiple terms by introducing an individual slack
weighting matrix for each term, which can be optimized to reduce the
conservatism. With the help of the multiple Jensen inequalities and by
developing a novel linearizing technique, two novel Lyapunov functional based
approaches are established to obtain sufficient stability conditions expressed
by linear matrix inequalities (LMIs). It is shown that these new conditions are
always less conservative than the existing ones. Moreover, by the positive
operator theory, a single LMI based condition and a spectral radius based
condition are obtained based on an existing sufficient stability condition
expressed by coupled LMIs. A numerical example illustrates the effectiveness of
the proposed approaches.Comment: 14 page
Spin transverse force and intrinsic quantum transverse transport
The spin-orbit coupling may generate spin transverse force on moving electron
spin, which gives a heuristic picture for the quantum transverse transport of
electron. A relation between the spin and anomalous Hall conductance and spin
force was established, and applied to several systems. It was predicted that
the sign change of anomalous Hall conductance can occur in diluted magnetic
semiconductors of narrow band and can be applied to identify intrinsic
mechanism experimentally
On symmetric differences of NP-hard sets with weakly P-selective sets
AbstractThe symmetric differences of NP-hard sets with weakly-P-selective sets are investigated. We show that if there exist a weakly-P-selective set A and an NP-⩽Pm-hard set H such that H - AϵPbtt(sparse) and A — HϵPm(sparse) then P = NP. So no NP-⩽Pm-hard set has sparse symmetric difference with any weakly-P-selective set unless P = NP. The proof of our main result is an interesting application of the tree prunning techniques (Fortune 1979; Mahaney 1982). In addition, we show that there exists a P-selective set which has exponentially dense symmetric difference with every set in Pbtt(sparse)
- …