A Study On Robust Control For Uncertain Linear Delay Systems

The accurate mathematics model for the practical control objects can hardly be obtained during analysis and study on control systems. Because of the changing of outside environment and other immeasurable disturbances, the model is usually different to the real plant. Usually, these differences can be described as the uncertainties in the model arguments. In addition, time-delay, which leads to non-stabilization and decline of dynamic performance, exists in many industrial systems. So, the research on the uncertain systems with time-delay has theoretic and practical significance and has attracted considerable attention in the control theory literatures all along.Presently, although there are many results about these problems, for uncertain linear systems with time-varying delays both in state and input, model transformation method is always used in literatures and the results are more conservative. This master thesis focuses on robust controller's design considering two conditions: system matrices can be controlled and can not be controlled. The main contents of this paper are outlined as follows:(1) The problem of robust H_∞control for uncertain linear systems with time-varyingdelays both in state and input and with controlled system matrices is investigated. Combined with new quadratic term integral inequality, the delay-dependent H_∞controller is derivedbased on constructing the Lyapunov-krasovskii function with the information of the lower and upper bounds of delay, in which the relationship between the time-varying delay and its lower and upper bounds are considered. Compared with the existed H_∞control method, theemulation result shows this method is less conservative than existed literatures.(2) The problem of robust control for uncertain linear systems with time-varying delays both in state and input and with uncontrolled system matrices is investigated. A new Lyapunov-krasovskii function is proposed by considering the relationship between cross terms combined with new quadratic term integral inequality. A robust stability criterion is proposed based on LMI; further, a robust memoryless state-feedback controller is derived by the criterion. Through theoretic analysis and emulation, the obtained controllers are less conservative than the existed representative methods especially for systems with time-varying input delay and state delay respectively.