Observer-Based Controller for a Class of Linear Discrete-Time Descriptor Systems

In this paper, we develop a novel method to design an observer-based controller for a class of linear discrete-time descriptor systems. The idea of the proposed approach is based on the separation between dynamic and static relations of the descriptor model. As the observer and the controller are both designed to be individually stable, the closed-loop state system will also be stable, and the separation property will hold. The convergence of the closed-loop state system is studied by using the Lyapunov theory. Besides, the convergence condition is given in term of Linear Matrix Inequality (LMI). Finally, an application based on heat exchanger pilot process is presented as an illustrative example to show the performance of the proposed dynamic controller design.