Robust stability test for 2-D continuous-discrete systems with interval parameters

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.

Numerical simulation of avascular tumor growth based on p27 gene regulation

A multi-scale continuous-discrete model based on the effects of the p27 gene control is built to simulate the avascular tumor growth. At the tissue level, the continuous Eulerian model is adopted to determine the distribution of the concentration of oxygen, the extracellular matrix （ECM）, and the matrix-degradative enzyme （MDE）. At the cellular level, the discrete Lagrangien model is adopted to determine the movement, the proliferation, and the death of single tumor cells （TCs）. At the genetic level, whether a cell is committed to mitosis is determined by solving a set of equations modeling the effects of the p27 gene control. The avascular morphological evolution of the solid tumor growth is simulated, including the radius the oxygen distribution over time, and the expression. of the solid tumor, the number of the TCs, inhibiting effect＇ of the up-regulating p27 gene

Accurate estimation of line-of-sight rate under strong impact interference effect

In the process of the terminal guidance of a kinetic kill vehicle(KKV),it is very important to accurately estimate the lineof-sight(LOS)rate via the measurements of a target seeker onboard the KKV.The strong impact interference caused by the large lateral thrust produced by the thrusters on the KKV is a main factor that affects the measurements on the LOS angle.A method to estimate the impact interference and the LOS rate together via a Kalman filter is proposed to improve the estimation precision of the LOS rate.The observability of the system describing the missile-target relative motion model and the impact interference model is proved,and then a Kalman filter is designed.In the Kalman filter design,the continuous-discrete and two-stage filtering techniques are used because the system model is time-variant and high-order.Numerical simulation results show that by estimating the impact interference,the estimation precision of the LOS rate is increased,and so the miss distance of the KKV under the strong impact interference is reduced.The proposed continuous-discrete two-stage Kalman filter shows higher estimation precision and lower computational cost than the naive discrete augmented state Kalman filter.