Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

This paper is concerned with the problem of stabilization of the Roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Non-equilibrium between ions and electrons inside hot spots from National Ignition Facility experiments

The non-equilibrium between ions and electrons in the hot spot can relax the ignition conditions in inertial confinement fusion[Fan et al.,Phys.Plasmas 23,010703(2016)],and obvious ion-electron non-equilibrium could be observed by our simulations of high-foot implosions when the ion-electron relaxation is enlarged by a factor of 2.On the other hand,in many shots of high-foot implosions on the National Ignition Facility,the observed X-ray enhancement factors due to ablator mixing into the hot spot are less than unity assuming electrons and ions have the same temperature[Meezan et al.,Phys.Plasmas 22,062703(2015)],which is not self-consistent because it can lead to negative ablator mixing into the hot spot.Actually,this non-consistency implies ion-electron non-equilibrium within the hot spot.From our study,we can infer that ion-electron non-equilibrium exists in high-foot implosions and the ion temperature could be~9%larger than the equilibrium temperature in some NIF shots.

On designing memory state feedback controller for linear systems with interval time-varying delay

This paper is concerned with the design of a memory state feedback controller for linear systems with interval time-varying delays.The time delay is assumed to be a time-varying continuous function belonging to a given interval,which means that the lower and upper bounds of time-varying delay are available.First,a less conservative delay-range-dependent stability criteria is proposed by using a new interval fraction method.In the process of controller synthesis,the history information of system is considered in the controller design by introducing the lower delay state.Moreover,the usual memoryless state feedback controller for the underlying systems could be considered as a special case of the memory case.Finally,two numerical examples are given to show the effectiveness of the proposed method.