The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state an...The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].展开更多
In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this s...In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to ap3 （the result of the maximum momentum assumption） and a2p4 （the result of the minimum length assumption）, where a - 1/MpIc is the GUP parameter. On the basis of the work by Ali et al., we solve the generaiized Schrodinger equation which is extended to include the a2 correction term, and find that the length L of the finite potentiai well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of aolp1 in GUP scenario.展开更多
基金Project(12511109) supported by the Science and Technology Studies Foundation of Heilongjiang Educational Committee of 2011, China
文摘The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].
基金Supported by National Natural Science Foundation of China under Grant Nos.10865003 and 11464005
文摘In this article, we apply the Generalized Uncertainty Principle （GUP）, which is consistent with quantum gravity theories to an elementary particle in a finite potential well, and study the quantum behavior in this system. The generalized Hamiltonian contains two additional terms, which are proportional to ap3 （the result of the maximum momentum assumption） and a2p4 （the result of the minimum length assumption）, where a - 1/MpIc is the GUP parameter. On the basis of the work by Ali et al., we solve the generaiized Schrodinger equation which is extended to include the a2 correction term, and find that the length L of the finite potentiai well must be quantized. Then a generalization to the double-square-well potential is discussed. The result shows that all the measurable lengths especially the distance between the two potential wells are quantized in units of aolp1 in GUP scenario.
