D. K. Arif, . and Fatmawati, . and D. Adzkiya, . and Mardlijah, . and H. N. Fadhilah, . and P. Aditya, . (2019) Analysis of the Model Reduction Using Singular Perturbation Approximation on Unstable and NonMinimal DiscreteTime Linear Systems and Its Applications. Nonlinear Dynamics and Systems Theory, 19 (3). pp. 362371. ISSN 15628353, 18137385
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Abstract
In the natural phenomena, many systems are unstable and nonminimal. Moreover, the systems in the universe often have large order. Therefore, we need to simplify the order of the system without any significant errors. Simplification of this system can be done using the reduction of the model. Model reduction can only be done on the stable and minimal system. Thus, we need a model reduction for unstable and nonminimal systems. There are many model reduction methods in the literature, for example, a balanced truncation method and a singular perturbation approximation. In this work, we propose a method to reduce unstable and nonminimal systems by using the singular perturbation approximation (SPA). First, we decompose the unstable system into a stable subsystem and an unstable subsystem. Then, if the stable subsystem is nonminimal, we apply the minimization process to obtain a stable subsystem that is minimal. Next, we apply the singular perturbation approximation to the stable and minimal subsystem to obtain a reduced subsystem. Finally, we obtain a total reduced model by combining the unstable subsystem and the reduced subsystem. Then we apply the method to shallow water equations. Based on the simulation results, frequency response of the original system and the reduced minimal system using the SPA method has similarity in low frequency, but in high frequency the value tends to be different. Furthermore, the error bound of the SPA and the balanced truncation method is almost the same
Item Type:  Article  

Uncontrolled Keywords:  model reduction; singular perturbation approximation; unstable systems; nonminimal systems  
Subjects:  Q Science Q Science > QA Mathematics Q Science > QA Mathematics > QA370387 Differential Equations 

Divisions:  08. Fakultas Sains dan Teknologi > Matematika  
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Depositing User:  Mr Vega Andi Budiman  
Date Deposited:  22 Mar 2022 14:48  
Last Modified:  22 Mar 2022 14:48  
URI:  http://repository.unair.ac.id/id/eprint/114275  
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