Robust control for time-delay systems with uncertainties

Abstract

Time delays happen commonly in various engineering systems. Transportation and measurement lags, computation and analysis times, and communication lags all introduce delays into control loops. The presence of delays in systems greatly complicates the analysis and the design of feedback controllers for such systems. In many practical systems, it is difficult to develop accurate mathematical descriptions of them. Thus there are inevitable uncertainties in their constructed model. These uncertainties consist of unknown or imperfectly known parameter values and nonlinearities of the controlled systems as well as disturbances from the external environment. These problems can be resulted in poor performances and instability. This dissertation addresses the inherent problems for systems with delays in control in the presence of unknown uncertainties. For systems with delayed state only, required control input enters systems without delay and so the systems are also stabilized immediately by the designed control law. However, systems with delays in controls have control loops with each delay periods and so are stabilized by the required control law after the delayed interval. If there are unknown uncertainties in these systems, the resulting uncertainties cannot be handled by the required control law during the delay interval because of lack of information and causality of them. These inherent problems eventually affect the stability and performances of the closed-loop system. Thus, the uncertain input-delay systems can have a maximum delay bound such that the system is globally asymptotically stable. The objectives of this thesis are to design a controller for robust stabilization of uncertain linear systems with delay in control variables, and to determine a maximum delay size so that the system is globally asymptotically stable. In thesis, the state feedback control scheme with delay compensation is used for robust stabilization and maximization of delay size of unc...