Exponential stability of cellular neural networks with multiple time delays and impulsive effects

In this work, the stability issues of the equilibrium points of the cellular neural networks with multiple time delays and impulsive effects are investigated. Based on the stability theory of Lyapunov-Krasovskii, the method of linear matrix inequality （LMI） and parametrized first-order model transformation, several novel conditions guaranteeing the delaydependent and the delay-independent exponential stabilities are obtained. A numerical example is given to illustrate the effectiveness of our results.

Three-dimensional arterial spin labeling and diffusion kurtosis imaging in evaluating perfusion and infarct area size in acute cerebral ischemia

BACKGROUND Early thrombolytic therapy is crucial to treat acute cerebral infarction,especially since the onset of thrombolytic therapy takes 1-6 h.Therefore,early diagnosis and evaluation of cerebral infarction is important.AIM To investigate the diagnostic value of magnetic resonance multi-delay threedimensional arterial spin labeling(3DASL)and diffusion kurtosis imaging(DKI)in evaluating the perfusion and infarct area size in patients with acute cerebral ischemia.METHODS Eighty-four patients who experienced acute cerebral ischemia from March 2019 to February 2021 were included.All patients in the acute stage underwent magnetic resonance-based examination,and the data were processed by the system’s own software.The apparent diffusion coefficient(ADC),average diffusion coefficient(MD),axial diffusion(AD),radial diffusion(RD),average kurtosis(MK),radial kurtosis(fairly RK),axial kurtosis(AK),and perfusion parameters post-labeling delays(PLD)in the focal area and its corresponding area were compared.The correlation between the lesion area of cerebral infarction under MK and MD and T2-weighted imaging(T2WI)was analyzed.RESULTS The DKI parameters of focal and control areas in the study subjects were compared.The ADC,MD,AD,and RD values in the lesion area were significantly lower than those in the control area.The MK,RK,and AK values in the lesion area were significantly higher than those in the control area.The MK/MD value in the infarct lesions was used to determine the matching situation.MK/MD<5 mm was considered matching and MK/MD≥5 mm was considered mismatching.PLD1.5s and PLD2.5s perfusion parameters in the central,peripheral,and control areas of the infarct lesions in MK/MD-matched and-unmatched patients were not significantly different.PLD1.5s and PLD2.5s perfusion parameter values in the central area of the infarct lesions in MK/MD-matched and-unmatched patients were significantly lower than those in peripheral and control areas.The MK and MD maps showed a lesion area of 20.08±5.74 cm^(2) and 22.09±5.58 cm^(2),respectively.T2WI showed a lesion area of 19.76±5.02 cm^(2).There were no significant differences in the cerebral infarction lesion areas measured using the three methods.MK,MD,and T2WI showed a good correlation.CONCLUSION DKI parameters showed significant difference between the focal and control areas in patients with acute ischemic cerebral infarction.3DASL can effectively determine the changes in perfusion levels in the lesion area.There was a high correlation between the area of the infarct lesions diagnosed by DKI and T2WI.

Solution of Multi-Delay Dynamic Systems by Using Hybrid Functions

In this paper, we present a method for finding the solution of the linear multi-delay systems (MDS) by using the hybrid of the Block-Pulse functions and the Bernoulli polynomials. In this approach, the MDS is reduced to a system of linear algebraic equations by expanding various time functions for the hybrid functions and using operational matrices. To demonstrate the validity and the applicability of the technique, some examples are presented.

Stabilizing Decomposition of neutral Linear Time－invariant Large－Scale Control Systems With Multi－group Multi－delays

By the way of Introducing some parameters εi(i = 1, 2, 3), a result for the stabilization of the linear time-invariant isolated control subeystems without the time delays imply the stabilization of the neutral linear time-invariant large-scale control systems with the multigroup multi-delaysis improved using Lyapunov decomposition equivalence method found by Liu Yongqing. These results in this paper can be expanded the stabilization region of the parameters to be 6 times of the former stable range of the parameters.

STABILITY OF N-DIMENSIONAL LINEAR SYSTEMS WITH MULTIPLE DELAYS AND APPLICATION TO SYNCHRONIZATION

This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore （2002）. Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua＇s systems.

A multi-order method for predicting stability of a multi-delay milling system considering helix angle and run-out effects

In this paper, a multi-delay milling system considering helix angle and run-out effects is firstly established. An exponential cutting force model is used to model the interaction between a work-piece and a cutting tool, and a new approach is presented for accurately calibrating exponential cutting force coefficients and cutter run-out parameters. Furthermore, based on an implicit multi-step Adams formula and an improved precise time-integration algorithm, a novel stability prediction method is proposed to predict the stability of the system. The involved time delay term and periodic coefficient term are integrated as a comprehensive state term in the integral response which is approximated by the Adams formula. Then, a Floquet transition matrix with an arbitraryorder form is constructed by using a series of matrix multiplication, and the stability of the system is determined by the Floquet theory. Compared to classical semi-discretization methods and fulldiscretization methods, the developed method shows a good performance in convergence, efficiency,accuracy, and multi-order complexity. A series of cutting tests is further carried out to validate the practicability and effectiveness of the proposed method. The results show that the calibration process needs a time of less than 5 min, and the stability prediction method is effective.