Abstract—The author presented a method for model order reduction of large-scale time-invariant systems in time domain. In this approach, two modified Hankel matrices are suggested for getting reduced order models. The proposed method is simple, efficient and retains stability feature of the original high order system. The viability of the method is illustrated through the examples taken from literature. Keywords—Model Order Reduction, Stability, Hankel Matrix, Time-Domain, Integral Square Error. I. INTRODUCTION ODEL order reduction is a very attractive idea in CAD area. It replaces the original large scale systems model with a much smaller one, yet still retains the original behavior under investigation to high accuracy. Therefore, by simulating just the reduced small system one can still study the original system and thus make the design work much easier. With the ever increasing the scale of system models appearing in the engineering design practice, model order reduction has become an indispensible tool in numerous areas of science and technology. Model order reduction is also a very interesting and meaningful mathematical problem in its own right. Several methods based on Hankel matrix have been used for deriving low order state models from a given complex system described by its transfer function matrix or state model. The problem of minimal realization of rational transfer function matrix based on Hankel matrix approach has drawn major attention of the several authors [1]-[7] from the last few decades. Rozsa et al. [2], Hickin & Sinha [5] and Shrikhande et al. [6], etc. has suggested reduction methods based on Hankel matrix approach in which Hankel matrix is converted into Hermite normal form by using outer products. The minimal realization can be achieved in fixed number of operations on the Hankel matrix. Shamash [3] has proposed a method based on Hankel matrix approach in which conversion of Hankel matrix into Hermite normal form is not required but using Silverman’s algorithm [8] and the theory developed in reference [1], the reduced order state models are obtained by minimal realization. The method suggested by Shamash is applicable to linear SISO and MIMO dynamic systems. In this paper, the outer products algorithm is used to synthesize the reduced model which is equally applicable to linear multi- variable system as well. Dr. C.B Vishwakarma is with the Galgotias College of Engineering & Technology, Greater Noida, 201306 India (phone: 0120-4513800; fax: 0120- 4513888; e-mail: cbvishwa@ gmail.com). II. PROBLEM STATEMENT Let the th n order original high order linear SISO system be expressed as () () () () () Xt AX t BU t Yt CX t • ⎫ ⎪ = + ⎬ = ⎪ ⎭ (1) where () X t , () U t and () Y t are state, input and output variable vectors and 1 [ ] , [ ] n n n A B × × and 1 [ ] n C × are state, input, and output matrices of the original high order system. The problem is to find the th k ( ) k n < order reduced model, which reflects the dominant properties of the original high order system (1) be expressed as () () () () () k k k k k k k X t AX t BUt Y t CX t • ⎫ ⎪ = + ⎬ = ⎪ ⎭ (2) where () k X t , () k Y t are reduced state and output vectors and () k Y t is close approximation of () Y t and 1 [ ] , [ ] k k k A B × × , and 1 [ ] k C × are unknown matrices of the reduced order model. III. DESCRIPTION OF THE METHOD The transfer function () Gs , which can be expanded in power series of 1 s − or s as 1 () ( ) Gs C sI A B − = − (3) 1 2 3 1 2 3 .................. Ms Ms Ms − − − = + + + (4) 2 1 2 3 ....................... T Ts Ts = + + + (5) where 1 1, 2, 3, .......... i i i i M CA B i T CA B − − ⎫ = ⎪ = ⎬ = ⎪ ⎭ (6) and i M & i T are the th i Markov parameter and time-moment respectively. The following two modified Hankel matrices (0) ij H are defined in the following manner with i j n = = as C. B. Vishwakarma Modified Hankel Matrix Approach for Model Order Reduction in Time Domain M World Academy of Science, Engineering and Technology International Journal of Physical and Mathematical Sciences Vol:8, No:2, 2014 404 International Scholarly and Scientific Research & Innovation 8(2) 2014 scholar.waset.org/1307-6892/9997728 International Science Index, Physical and Mathematical Sciences Vol:8, No:2, 2014 waset.org/Publication/9997728