The Reduced Order Model Design and its Applications of Linear Discrete-Time Control Systems

Model reduction of linear control systems is an important area of research. Over the last few decades, various methods have been devised for the model reduction of linear control systems using transfer function approach and state-space approach. In this paper, we use state space approach to investigate the reduced order model design for the linear discrete-time control systems using the dominant state of the control systems and detail its applications, namely, the observer design of reduced order linear control systems using the dominant state approach. Our state-space approach of reduced order model design for large-scale discrete-time linear systems essentially uses the modal approach (Sundarapandian, 2005) for the model reduction of the original discrete-time linear control systems. As an application, we detail the exponential observer design for estimating the dominant state of the given discrete-time linear system. A numerical example has been provided to validate and illustrate the reduced order model result derived in this paper.