The Stability And Robust Control For Hamilton Systems With Time-delay And Saturation

In a practical project, systems are usually affected by a variety of external fac-tors including the time delay and saturation phenomenon which are the most com-mon. They also are the main reasons that cause instability and bad performance of systems, even more serious consequences. However, due to the systems are very complicated, it increases the difficulty of such control problem of nonlinear systems. There are still many fundamental problems that are difficult to get a good solution. The general Hamilton systems are a kind of important nonlinear systems. Its struc-ture and physical meaning are clear, and it shows obvious superiority in the stability analysis and control design problems. In recent years, Hamilton systems get more and more attention in control of nonlinear systems.For Hamilton system with actuator saturation, state time-delay and disturbance, this paper investigates stability and control design. The content mainly includes the following several aspects:· The limited L2 gain stabilization of the dissipative Hamilton systems with ac-tuator saturation is investigated, including the output stability and the input stability. Sufficient conditions are proposed, the corresponding closed-loop system is globally asymptotically stable with the static output feedback. More-over, with the evolution of nonlinear functions for the system, the closed-loop system can receive the L2 gain stabilization, while the estimated value of gain is obtained. Finally the simulation of an illustrative example shows that the proposed method is effective.· The limited L2 gain stabilization of the dissipative Hamilton systems subject to time-varying delay and actuator saturation is investigated. According to de-pending on time delay or not, conditions of the stability are divided into two categories: delay-dependent and delay-independent. Analyzed from the two aspects, the corresponding closed-loop system is globally asymptotically sta-ble with the static output feedback. Moreover, with the evolution of nonlinear functions for the system, the closed-loop system can receive the L2 gain stabi-lization, while the estimated value of gain is obtained. Finally the simulation of an illustrative example shows that the proposed method is effective.· The theoretical results obtained are applied in stabilization of the single-machine infinite power system. The limited gain stabilization of power system with both excitation and steam valve saturation is analyzed. Based on the Hamil-ton energy theory, the power system is changed into the corresponding gen-eralized dissipation Hamilton system. Under the sufficient conditions given and the static output feedback controller, the power system can achieve global asymptotic stability and the limited L2 gain stability. Simulation example is given to illustrate the effectiveness of the results.