NUST Institutions Library Catalogue

In the domain of control systems engineering, mathematical modeling constitutes the
cornerstone for the analysis of dynamical systems, particularly when systems become
increasingly complex. However, the computational demands of simulating large-scale
systems, incorporating various types of equations, present formidable challenges. Model
reduction techniques aim to approximate complex, high-order systems with simpler,
lower-order models while retaining acceptable accuracy. These techniques ultimately
simplify the design, modeling, and simulation of large-scale systems.
This dissertation delves into model reduction techniques tailored for large-scale highdimensional
systems, leveraging balanced structures for improving efficiency.
Initially, this research carries out literature review of existing model order reduction
techniques in order to examine their limitations. Over the past few decades, numerous
model order reduction methods have been proposed in the literature. Among these, the
balanced truncation method is widely adopted due to its simplicity, ability to preserve
stability in reduced models, and incorporation of a priori error bounds. The method
involves balancing the original system and subsequently truncating the least controllable
and observable states to derive reduced order models. However, in literature we find
disadvantages of balanced truncation approach, because in few of the cases, it fails
to guarantee the positive definiteness of associated Gramians, leading to potential
instability in reduced models. To address this limitation, several alternate methods have
also been proposed in the literature. However, these methods often impose restrictive conditions and may introduce significant approximation errors. Few of these, prove
realization-dependent; while others increase computationally complexity, hindering their
practical usage.