In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate time...In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.展开更多
Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytop...Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.展开更多
文摘In this paper, the Non-Commutative phase space and Dirac equation, time-dependent Dirac oscillator are introduced. After presenting the desire general form of a two-dimensional linear dependency on the coordinate timedependent potential, the Dirac equation is written in terms of Non-Commutative phase space parameters and solved in a general form by using Lewis–Riesenfield invariant method and the time-dependent invariant of Dirac equation with two-dimensional linear dependency on the coordinate time-dependent potential in Non-Commutative phase space has been constructed, then such latter operations are done for time-dependent Dirac oscillator. In order to solve the differential equation of wave function time evolution for Dirac equation and time-dependent Dirac oscillator which are partial differential equation some appropriate ordinary physical problems have been studied and at the end the interesting result has been achieved.
基金This work was supported by the National Natural Science Foundation of China(No.60574084)the National 863 Project(No.2006AA04Z428)the National 973 Program of China(No.2002CB312200).
文摘Robust H-infinity filtering for a class of uncertain discrete-time linear systems with time delays and missing measurements is studied in this paper. The uncertain parameters are supposed to reside in a convex polytope and the missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Our attention is focused on the analysis and design of robust H-infinity filters such that, for all admissible parameter uncertainties and all possible missing measurements, the filtering error system is exponentially mean-square stable with a prescribed H-infinity disturbance attenuation level. A parameter-dependent approach is proposed to derive a less conservative result. Sufficient conditions are established for the existence of the desired filter in terms of certain linear matrix inequalities （LMIs）. When these LMIs are feasible, an explicit expression of the desired filter is also provided. Finally, a numerical example is presented to illustrate the effectiveness and applicability of the proposed method.
