The delay systemx·(t)=Ax(t)+Bx(t-r)is considered. The necessary and sufficient conditions of the existence of a kind of Liapunov functional for the system are given.
The fundamental problem of an elastic-plastic body subjected to incremental loading is reviewed using a compact internal variable approach based on work carried out at the University of Cape Town in which a quadratic ...The fundamental problem of an elastic-plastic body subjected to incremental loading is reviewed using a compact internal variable approach based on work carried out at the University of Cape Town in which a quadratic functional was developed for the free energy using Taylor series. Now the departure from that approach is the focus on developing the Liapunov function for the nonlinear differential equations of motion. Static and dynamic equations of motion are derived and shown to meet the requirements of the Liapunov function. As a consequence, time integration parameters that are used in the discrete formulations are easily obtained based on the same requirements. The resulting generalized Newton-Raphson scheme is stable in the sense of Liapunov＇s direct method.展开更多
The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control...The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control systems which have quadric performance index via Liapunov method.展开更多
文摘The delay systemx·(t)=Ax(t)+Bx(t-r)is considered. The necessary and sufficient conditions of the existence of a kind of Liapunov functional for the system are given.
文摘The fundamental problem of an elastic-plastic body subjected to incremental loading is reviewed using a compact internal variable approach based on work carried out at the University of Cape Town in which a quadratic functional was developed for the free energy using Taylor series. Now the departure from that approach is the focus on developing the Liapunov function for the nonlinear differential equations of motion. Static and dynamic equations of motion are derived and shown to meet the requirements of the Liapunov function. As a consequence, time integration parameters that are used in the discrete formulations are easily obtained based on the same requirements. The resulting generalized Newton-Raphson scheme is stable in the sense of Liapunov＇s direct method.
文摘The controlled objects are uncertain stable,but the optimal control systems which are constituted by the controlled objects under certain conditions are certain stable. This paper analyses stability of optimal control systems which have quadric performance index via Liapunov method.
