Stability preseving frequency limited model reduction techniques

Abstract

Model order reduction is the very challenging field of control system because the order of higher order system is reduce by using MOR. The mathematical models of high order dynamic systems can be described in different form either in state space or transfer function. These are expressed in time and frequency domain respectively. It is generally recommended for reducing the system order by maintaining the dominant properties of the original system. It will promote to make better understanding of physical system, computational and hardware complexities reduces and simplify the controller design. Ample amount of research have been done on model order reduction. Some existing methods reducing the full order system into a lesser order for a entire frequency ranges. However, there are some applications like controller and filter etc that require reduction over specific frequency band. That gives the basic for the using frequency weights in model order reduction. Moreover, prior frequency limited techniques have drawbacks of lacking properties such as stability, error bound and large approximation error. This thesis will focus on frequency limited model reduction problem. Firstly, problem of frequency limited MOR will be formulated and then novel frequency limited balanced MOR methods are purposed. These methods will yield stable reduced order models. The new measures will guarantee stability by specifying some fictitious semi positive/ positive definiteness of input and output related matrices. Each input and output matrices preserved positive definiteness of the matrices, respectively, by defining new controllability Gramian and observability Gramian in a novel way. That guides towards a new transformation matrix which subsequently, results in stability preserving methods including computable error bounds and has a low approximation error.