Stability And Control Design For A Class Of Nonlinear Descriptor System With Time-delay

The descriptor system is a natural representation of dynamic systems and describes a larger class of systems than the normal system model. In the last three decades, the descriptor system has received a great deal of attention, and many studies have been devoted to the stabilization of linear descriptor systems. Time delays are frequently encountered in various engineering systems such as aircraft. Long transmission lines in pneumatic systems, and chemical or process control systems. It has been shown that the existence of time delays is often one of the main causes of instability and poor performance of a control system. Therefore, systems with time delays have attracted a great deal of attention over the past few years.This paper addresses the existence and uniqueness of a solution and stability for Lipschitz discrete-time descriptor systems with time-delay. By means of the fixed point principle and Schur’s lemma, a criterion is presented via a matrix inequality, and the criterion guarantees the existence and uniqueness of a solution. In addition, a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously. Then, a necessary and sufficient condition is presented to ensure that the system is generalized quadratic stabilization via the design of the feedback controller. Meanwhile, a LMI approach is also presented to get the feedback controller. So that it is convenient to use LMI toolbox. Finally, the approach is illustrated by numerical examples.