Development of Model Order Reduction Techniques

Mathematical modeling is an essential feature for the analysis and design of a dynamical system. Generally, large and complex models are obtained from physical systems. Some ex- amples are robotic, telecommunications, network, mechanical and many other complex sys- tems. These systems are governed by the partial differential, Laplace and integro-differential equations etc. For the analysis and design of such systems, reduced order models are desir- able that provide a good approximation of the original systems. In last few decades, notable research work has been done on different aspects of model reduction. Existing techniques of model order reduction mostly suffer from the limitation of absence of original system key properties in reduced order system like passivity, stability, large approximation error and lack of a priori error bounds etc. This thesis investigates frequency weighted balanced model order reduction problem for standard and generalized (singular and non-singular), continuous and discrete linear time invariant systems. Firstly the frequency weighted model reduction problem is formulated. New frequency weighted model order reduction techniques are proposed for standard continuous and dis- crete time systems. Frequency interval Gramians based model order reduction techniques (where weights are not explicitly predefined) are also presented for standard continuous and discrete time systems. The proposed techniques guarantee stability even for the case where double sided weightings are employed. A priori frequency response error bounds are also de- rived. The proposed techniques yield mostly low frequency response error when compared to well known existing frequency weighted model reduction techniques. A generalization of existing frequency interval Gramians based model reduction tech- niques for Generalized non-singular discrete and continuous time systems is also presented. Moreover, a frequency limited model reduction technique for Generalized descriptor system is also presented. Simple algorithms are also given for preserving the stability of reduced- order models. The work also extends Poor Man’s truncated balanced realization for fre- quency limited case. Numerical examples are also presented for comparison of generalized techniques. Finally, new techniques to address time interval Gramians based model reduction are also presented for standard continuous time systems. The proposed techniques yield easily com- putable error bounds and comparable frequency response error.