Abstract:
The objective of this thesis is to originate new techniques of model order
reduction for single input single output (SISO), multi-input multi-output (MIMO)
continuous and discrete time interval systems and compare them with existing
techniques. This has been attempted for systems described by transfer function
models. Existing model reduction methods for fixed coefficients have been extended
to interval systems in frequency domain. The developed methods have intuitive
appeal and compare favourably with available techniques. These methods remove
some of the inherent difficulties associated with existing model order reduction
methods of interval systems. The performance of the original system and reduced
order system is examined.
The reduced order interval models obtained by the extension of fixed
coefficients reduction techniques to interval systems may suffer from the following
drawbacks.
(1) The reduced interval models may be unstable though the original interval
system is stable.
(2) It may exhibit non minimum phase characteristics.
(3) The reduced interval models produce low accuracy in the mid and high
frequency ranges.
The proposed methods in the thesis are devoid of these drawbacks. The following
advantages are there using proposed methods
(1) The error approximation is small.
(2) The proposed techniques conserve the original system characteristics such
as stability.
(3) The proposed methods are computationally efficient.
The thesis is organised as under:
The introductory first chapter is followed by a review of stability analysis of an
interval system included in the second chapter. A review of frequency domain interval
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system model order reduction techniques are given in the third chapter. This chapter
also discuss the reasons for failures of extending Routh approximation to interval
systems. New mixed methods developed for model reduction of continuous time
interval systems are given in chapter four. This chapter also shows the advantage of
new techniques when compared with existing reduction techniques for interval
systems. In Chapter 5, two modified methods are proposed based on differentiation
method and Schwarz approximation method considering dependency property.
Chapter six elaborates new methods for the reduction of discrete time interval
systems. In chapter 7, interval plant stabilization by using stability boundary locus is
discussed briefly. The concluding chapter highlights the contributions made in the
thesis.
