Layered Control Strategy Of Robust Stabilization For Uncertain Singular Systems

In the design of control system, the accurate mathematics model of controlled plant is required. However, in practice the accurate models of some plants are hard to be achieved, there are some uncertainties such as parameters uncertainties, various disturbance and unmodeled dynamics, etc. Robust control exactly studies for uncertainty system by designing controller to stabilize the closed loop systems and meeting the demanded dynamic performance index. Descriptor system is a kind of dynamic system which has a more general description form and a wide application background. Many real systems can be described more accurate and convenient by using descriptor system model. In recent years, the theoretics and applications of the descriptor system has attracted the attention of many domestic and foreign scholars. And many results of regular system are extended to descriptor system.In this essay, the problem of robust stability for descriptor uncertain system both in continuous time and discrete time is studied. The hierarchical state feedback controllers are designed dependent on the states can be detected. Furthermore when the states cannot be measured, the hierarchical dynamic output feedback controllers are obtained. The conditions of the existing robust hierarchical controllers are given by a set of LMIs and the theoretical bases of hierarchical robust control are pointed out. The main results are as follows.First, based on the measured states, the issue of robust stabilization for descriptor uncertain system by hierarchical state feedback using Lyapunov stability theory and LMIs approach is studied. When there are uncertain parameters in system matrix and uncertain parameters both in system matrix and input matrix, the criterions of the existing robust hierarchical controllers are given in terms of LMIs, respectively. Following, the theory of hierarchical robust control is pointed out. At last, numerical example is given to illustrate its feasibility.Second, Assumed that the states cannot be measured, based on Lyapunov stability theory and LMIs, robust hierarchical dynamic output controllers are designed to make sure the uncertainty descriptor system being stable. When there are uncertainties in system matrix and there are uncertainties in system matrix, input matrix and output matrix, the conditions of the exiting output controllers are obtained, respectively. Also, the theory of hierarchical robust control is pointed out. Numerical example is given to illustrate the feasibility of the methods.Finally, when the states can be detected, the problem of robust stabilization for discrete descriptor uncertain system by hierarchical state feedback is discussed. The situation of system matrix contains uncertainties is considered. The criterion is given by a group of LMIs and the theory of hierarchical robust control is identified. An example shows effectiveness of the proposed strategy.