Tracking Control Of Discrete Time Systems With Multiple Delays

The research of time delayed systems attracts considerable attention, because time delays which may degrade the performance of systems and lead to instability exists widely in various control systems. Tracking control being applied extensively in engineering practice shows an important practical prospect in time delayed system study field in recently years. This dissertation focuses on solving output tracking control problems for discrete-time systems with multiple time-varying delays. There are three main points studied as follows:(1) The mixed H2/H∞ output tracking control problem is studied for discrete time systems with multiple time varying delays. Based on Lyapunov stability theory, free weight matrix method and Linear Matrix Inequality(LMI) technology, a delay dependent sufficient condition is presented to guarantee the asymptotic stability and mixed H2/H∞ performance. Then, the relevant non-convex problem is transformed to nonlinear programming problem by using cone comlementarity linearization(CCL) method. Finally, a tracking controller is obtained by means of Matlab LMI toolbox.(2) Observer based H∞ output tracking control problem is studied for discrete time systems with multiple time varying delays. By constructing the full order observer, states can be estimated for tracking controller, and a delay dependent sufficient condition is developed to guarantee the exponentially stability and H∞ output tracking performance. By means of CCL algorithm and Matlab LMI toolbox, state observer and tracking controller are obtained.(3) Composite disturbance observer-based control(DOBC) and H∞ output tracking control problem is studied for uncertain discrete time systems with multiple time varying delays. A disturbance observer is constructed to estimate disturbance of input. A delay dependent sufficient condition is deduced to guarantee the robust asymptotic stability and H∞ output tracking performance. The disturbance observer and tracking controller are solved by proposed algorithm.