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Estimating Numerical Error Bound for Unstable Dynamical Linear Systems
(Sanad HajMohammed, 2020-01-08) HajMohammed, Sanad
Many of the physical, chemical and engineering applications lead to a system of differential equations or partial differential equations. Some of those applications involve a high order system. In this work, we will present some important analytical and numerical results concerning linear dynamical systems and their applications. We consider the case of unstable linear dynamical systems and our goal is to reduce the order of this system with minimal error bound with zero initial condition. First, we present the stable system and study two approaches to reduced order of stable system, balanced truncation method and singular perturbation approximation method. Then we study the L_(2[0,T],ind) norm to reduce the order of unstable system. Next, to show the efficiency of these approaches we use MATLAB software to solve an example of stable system by balanced truncation method and another example of unstable system by L_(2[0,T],ind) norm.